The failure criteria and cumulative damage models, become therefore, an invaluable set of tools to the design against failure of laminate components. This design with the use of CLT can provide optimum laminates that have the desired stacking sequence to optimize mechanical properties and weight, as well as cost requirements. However, the discussion of this chapter did not account for failure that is not mechanical. The failure modes discussed concentrate on matrix or fiber cracking, debonding, and delamination, which was not examined at the laminate level. However, thermal and hygral effects are only accounted for in CLT and are not part of the failure criteria presented in this chapter. As a result, when failure is due to chemical degradation of the matrix under UV rays, or creep which should involve the time parameter, failure should be considered using different models which were not the scope of this chapter.

## Nomenclature

## Author details

only mechanical failure in the composite, can be applied to laminates of more than one constituents, as well as hybrid composite laminates. Therefore, if the optimization of a component requires more than one matrix and/or reinforcing phase, the above analysis could be followed to get estimates for the onset of failure and fatigue life of the component. The same holds true for hybrid laminates, where a third material, usually a reinforcing phase, other than fibers, for example a metallic reinforcement, is introduced. As a result, the above criteria and models can see applications in current designs of new composite materials, as the components built in n-d printing where the structures have not only varying material orientations, but also

The failure criteria and cumulative damage models, become therefore, an invaluable set of tools to the design against failure of laminate components. This design with the use of CLT can provide optimum laminates that have the desired stacking sequence to optimize mechanical properties and weight, as well as cost requirements. However, the discussion of this chapter did not account for failure that is not mechanical. The failure modes discussed concentrate on matrix or fiber cracking, debonding, and delamination, which was not examined at the laminate level. However, thermal and hygral effects are only accounted for in CLT and are not part of the failure criteria presented in this chapter. As a result, when failure is due to chemical degradation of the matrix under UV rays, or creep which should involve the time parameter, failure should be considered using different models which were not the scope of this chapter.

material properties.

96 Failure Analysis and Prevention

Nomenclature

Eijkl Young's Modulus Gij Shear Modulus K Bulk Modulus

f Volume Fraction

vij Poisson's Ratio σij Stress Tensor εkl Strain Tensor

κij Curvature

o Mid-Surface Strains

βij Hygroscopic Coefficient

Aij Extension Stiffness Matrix

Q Stiffness Matrix

αij Coefficient of Thermal Expansion

εij

Roselita Fragoudakis

Address all correspondence to<EMAIL_ADDRESS>
Merrimack College, North Andover, MA, USA

## References

[10] Wambua P, et al. Natural fibers: Can they replace glass in glass fiber reinforced plastics? Composites Science and Technology. 2003;63:1259-1264

**Chapter 7**

Provisional chapter

**Failure Rate Analysis**

Failure Rate Analysis

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

Failure prediction is one of the key challenges that have to be mastered for a new arena of fault tolerance techniques: the proactive handling of faults. As a definition, prediction is a statement about what will happen or might happen in the future. A failure is defined as "an event that occurs when the delivered service deviates from correct service." The main point here is that a failure refers to misbehavior that can be observed by the user, which can either be a human or another computer system. Things may go wrong inside the system, but as long as it does not result in incorrect output (including the case that there is no output at all) there is no failure. Failure prediction is about assessing the risk of failure for some time in the future. In my approach, failures are predicted by analysis of error events that have occurred in the system. As, of course, not all events that have occurred ever since can be processed, only events of a time interval called embedding time are used. Failure probabilities are computed not only for one

DOI: 10.5772/intechopen.71849

point of time in the future, but for a time interval called prediction interval.

Failure prediction is one of the key challenges that have to be mastered for a new arena of fault tolerance techniques: the proactive handling of faults. As a definition, prediction is a statement about what will happen or might happen in the future. A failure means "an occurrence that

The main point here is that a failure derives of misbehavior that can be observed by the operator, which can either be a human or another computer system. Some things may go wrong inside the system, but as long as it does not eventuate in incorrect output (such as the system that there is no output at all) the system can run without failure. Failure prediction is about evaluation the risk of failure for some times in the future. In my viewpoint, analysis of

> © The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

© 2017 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Keywords: failure, component, analysis, reliability, probability

happens when the delivered service gets out from correct service."

http://dx.doi.org/10.5772/intechopen.71849

Fatemeh Afsharnia

Fatemeh Afsharnia

Abstract

1. Introduction

**Chapter 7**

Provisional chapter

## **Failure Rate Analysis**

Failure Rate Analysis

## Fatemeh Afsharnia

[10] Wambua P, et al. Natural fibers: Can they replace glass in glass fiber reinforced plastics?

[11] Corniere-Nicollier T, et al. Life cycle assessment of Biofibres replacing glass fibers as reinforcement in plastics. Resources, Conservation and Recycling. 2001;33:267-287 [12] Joshi SV, et al. Are natural fiber composites environmentally superior to glass fiber

[13] Dhakal HN, et al. Effect of water absorption on the mechanical properties of hemp fibre reinforced unsaturated polyester composites. Composites Science and Technology. 2007;

[14] Wotzel K, et al. Life cycle studies on hemp fiber reinforced components and ABS for

[15] Wang W. Study of moisture absorption in natural fiber plastic composites. Composites

[16] Fragoudakis R, et al. A computational analysis of the energy harvested by GFRP and NFRP laminated beams under cyclic loading. Procedia Engineering. 2017;200:221-228 [17] Fragoudakis R. Predicting the optimum Stackign sequence of fiber reinforced plastic laminated beams under bending. In: SAMPE Seattle 2017; 22 May - 24-05-2017; Seattle,

[18] Hashin Z, Rotem A. A cumulative damage theory of fatigue failure. Journal of Materials

[19] Broutman LJ, Sahu SA. Progressive damage of glass reinforced plastic during fatigue. In: 22nd Annual technical Conference, Reinforced Plastics/Composite Div.; 1969

[20] Salkind MJ. Fatigue of composites, composite materials: Testing and design. In: ASTM

[21] Epaarachi JA. A study on estimation of damage accumulation of glass fibre reinforced plastic (GFRP) composited under block loading situation. Composite Structures. 2006;75:

[23] Fragoudakis R, Saigal A. Predicting the fatigue life in steel and glass fibre reinforced plastics using damage models. Journal of Materials Science and Applications. 2011;2:

[24] Fragoudakis R, Saigal A. Using damage models to predict fatigue in steel and glass fibre reinforced plastics. Journal of Materials Science and Engineering with Advanced technol-

[22] Suresh S. Fatigue of Materials. Cambridge, UK: Cambridge University Press; 1998

STP 497: American Society for Testing Materials; 1972. p. 143–169

automotive parts. Angewandte Makromolekulare Chemie. 1999;272:121-127

Composites Science and Technology. 2003;63:1259-1264

reinforced composites? Composites: Part A. 2005;35:371-376

Science and Technology. 2006;66:379-386

Science and Engineering. 1978;34:147-160

67:1674-1683

98 Failure Analysis and Prevention

WA. 2017

88-92

596-604

ogies. 2011;3:53-65

Additional information is available at the end of the chapter Fatemeh Afsharnia

http://dx.doi.org/10.5772/intechopen.71849 Additional information is available at the end of the chapter

#### Abstract

Failure prediction is one of the key challenges that have to be mastered for a new arena of fault tolerance techniques: the proactive handling of faults. As a definition, prediction is a statement about what will happen or might happen in the future. A failure is defined as "an event that occurs when the delivered service deviates from correct service." The main point here is that a failure refers to misbehavior that can be observed by the user, which can either be a human or another computer system. Things may go wrong inside the system, but as long as it does not result in incorrect output (including the case that there is no output at all) there is no failure. Failure prediction is about assessing the risk of failure for some time in the future. In my approach, failures are predicted by analysis of error events that have occurred in the system. As, of course, not all events that have occurred ever since can be processed, only events of a time interval called embedding time are used. Failure probabilities are computed not only for one point of time in the future, but for a time interval called prediction interval.

DOI: 10.5772/intechopen.71849

Keywords: failure, component, analysis, reliability, probability

## 1. Introduction

Failure prediction is one of the key challenges that have to be mastered for a new arena of fault tolerance techniques: the proactive handling of faults. As a definition, prediction is a statement about what will happen or might happen in the future. A failure means "an occurrence that happens when the delivered service gets out from correct service."

The main point here is that a failure derives of misbehavior that can be observed by the operator, which can either be a human or another computer system. Some things may go wrong inside the system, but as long as it does not eventuate in incorrect output (such as the system that there is no output at all) the system can run without failure. Failure prediction is about evaluation the risk of failure for some times in the future. In my viewpoint, analysis of

© The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

error events that have occurred in the system can be called failure prediction. To compute breakdown probabilities, not only one point of time in the future, but a time interval called prediction interval are considered, simultaneously.

is the characteristic of breakdown occurrence frequency. In this context, failure rate analysis constitute a strategic method for integrating reliability, availability and maintainability, by using methods, tools and engineering techniques (such as Mean Time to Failure, Equipment down Time and System Availability values) to identify and quantify equipment and system failures that prevent the achievement of its objectives. At first we define common words

Failure Rate Analysis

101

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A failure occurs when a component is not available. The cause of components failure is different; they may fail due to have been randomly chosen and marked as fail to assess their effect, or they may fail because any other component that were depending on else has brake down. In reliability engineering, a Failure is considered to event when a component/system is

In reliability engineering, an error is said a misdeed which is the root cause of a failure.

In reliability engineering, a fault is defined as a malfunction which is the root cause of an error. But within this chapter, we may refer to a component failure as a fault that may be conducted to the system failure. This is done where there is a risk of obscurity between a failure which is occurring in intermediate levels (referred to as a Fault) and one which is occurring finally

The reliability of a machine is its probability to perform its function within a defined period with certain restrictions under certain conditions. The reliability is the proportional expression of a machine's operational availability; therefore, it can be defined as the period when a machine can operate without any breakdowns. The equipment reliability depends to failures frequency,

or λ(t)2 can be defined as "the foretasted number of times an item will break down in a determined time period, given that it was as good as new at time zero and is functioning at time t". This computed value provides a measurement of reliability for an equipment. This value is currently described as failures per million hours (f/mh). As an example, a component with a failure rate of 10 fpmh would be anticipated to fail 10 times for 1 million hours time period. The calculations of failure rate are based on complex models which include factors using specific component data such as stress, environment and temperature. In the prediction model,

. Reliability predictions are based on failure rates. Failure intensity

not doing its favorable performance and considered as being unavailable.

related to failure rate:

• Failure

• Error

• Fault

(referred to as Failure).

which is expressed by MTBF1

Mean time between failures.

Conditional failure rate.

2. Failure Rate

1

2

Failure rates and their projective manifestations are important factors in insurance, business, and regulation practices as well as fundamental to design of safe systems throughout a national or international economy. From an economic view point, inaction owing to machinery failures as a consequence of downtimes can be so costly. Repairs of broken down machines are also expensive, because the breakdowns consume resources: manpower, spare parts, and even loss of production. As a result, the repair costs can be considered as an important component of the total machine ownership costs. Traditional maintenance policies include corrective maintenance (CM) and preventive maintenance (PM). With CM policy, maintenance is performed after a breakdown or the occurrence of an obvious fault. With PM policy, maintenance is performed to prevent equipment breakdown. As an example, it is appeared that in developing countries, almost 53% of total machine expenses have spent to repair machine breakdowns whereas it was 8% in developed countries, that founding the effective and practicable repair and maintenance program could decreased these costs up to 50%.

The complex of maintenance activities, methodologies and tools aim to obtain the continuity of the productive process; traditionally, this objective was achieved by reviewing and substituting the critical systems or through operational and functional excess in order to guarantee an excess of productive capacity. All these approaches have partially emerged inefficiencies: redundant systems and surplus capacity immobilize capitals that could be used more Affordable for the production activities, while accomplishing revision policies very careful means to support a rather expensive method to achieve the demand standards. The complex of maintenance activities is turned from a simple reparation activity to a complex managerial task which main aim is the prevention of failure. An optimal maintenance approach is a key support to industrial production in the contemporary process industry and many tools have been developed for improving and optimizing this task.

The majority of industrial systems have a high level of complexity, nevertheless, in many cases, they can be repaired. Moreover historical and or benchmarking data, related to systems failure and repair patterns, are difficult to obtain and often they are not enough reliable due to various practical constraints. In such circumstances, it is evident that a good RAM analysis can play a key role in the design phase and in any modification required for achieving the optimized performance of such systems. The assessing of components reliability is a basic sight for appropriate maintenance performance; available reliability assessing procedures are based on the accessibility of knowledge about component states. Nevertheless, the states of component are often uncertain or unknown, particularly during the early stages of the new systems development. So for these cases, comprehending of how uncertainties will affect system reliability evaluation is essential. Systems reliability often relies on their age, intrinsic factors (dimensioning, components quality, material, etc.) and use conditions (environment, load rate, stress, etc.). The parameter defining a machine's reliability is the failure rate (λ), and this value is the characteristic of breakdown occurrence frequency. In this context, failure rate analysis constitute a strategic method for integrating reliability, availability and maintainability, by using methods, tools and engineering techniques (such as Mean Time to Failure, Equipment down Time and System Availability values) to identify and quantify equipment and system failures that prevent the achievement of its objectives. At first we define common words related to failure rate:

• Failure

error events that have occurred in the system can be called failure prediction. To compute breakdown probabilities, not only one point of time in the future, but a time interval called

Failure rates and their projective manifestations are important factors in insurance, business, and regulation practices as well as fundamental to design of safe systems throughout a national or international economy. From an economic view point, inaction owing to machinery failures as a consequence of downtimes can be so costly. Repairs of broken down machines are also expensive, because the breakdowns consume resources: manpower, spare parts, and even loss of production. As a result, the repair costs can be considered as an important component of the total machine ownership costs. Traditional maintenance policies include corrective maintenance (CM) and preventive maintenance (PM). With CM policy, maintenance is performed after a breakdown or the occurrence of an obvious fault. With PM policy, maintenance is performed to prevent equipment breakdown. As an example, it is appeared that in developing countries, almost 53% of total machine expenses have spent to repair machine breakdowns whereas it was 8% in developed countries, that founding the effective and practicable repair and maintenance program could decreased these costs

The complex of maintenance activities, methodologies and tools aim to obtain the continuity of the productive process; traditionally, this objective was achieved by reviewing and substituting the critical systems or through operational and functional excess in order to guarantee an excess of productive capacity. All these approaches have partially emerged inefficiencies: redundant systems and surplus capacity immobilize capitals that could be used more Affordable for the production activities, while accomplishing revision policies very careful means to support a rather expensive method to achieve the demand standards. The complex of maintenance activities is turned from a simple reparation activity to a complex managerial task which main aim is the prevention of failure. An optimal maintenance approach is a key support to industrial production in the contemporary process industry and many tools have been devel-

The majority of industrial systems have a high level of complexity, nevertheless, in many cases, they can be repaired. Moreover historical and or benchmarking data, related to systems failure and repair patterns, are difficult to obtain and often they are not enough reliable due to various practical constraints. In such circumstances, it is evident that a good RAM analysis can play a key role in the design phase and in any modification required for achieving the optimized performance of such systems. The assessing of components reliability is a basic sight for appropriate maintenance performance; available reliability assessing procedures are based on the accessibility of knowledge about component states. Nevertheless, the states of component are often uncertain or unknown, particularly during the early stages of the new systems development. So for these cases, comprehending of how uncertainties will affect system reliability evaluation is essential. Systems reliability often relies on their age, intrinsic factors (dimensioning, components quality, material, etc.) and use conditions (environment, load rate, stress, etc.). The parameter defining a machine's reliability is the failure rate (λ), and this value

prediction interval are considered, simultaneously.

oped for improving and optimizing this task.

up to 50%.

100 Failure Analysis and Prevention

A failure occurs when a component is not available. The cause of components failure is different; they may fail due to have been randomly chosen and marked as fail to assess their effect, or they may fail because any other component that were depending on else has brake down. In reliability engineering, a Failure is considered to event when a component/system is not doing its favorable performance and considered as being unavailable.

• Error

In reliability engineering, an error is said a misdeed which is the root cause of a failure.

• Fault

In reliability engineering, a fault is defined as a malfunction which is the root cause of an error. But within this chapter, we may refer to a component failure as a fault that may be conducted to the system failure. This is done where there is a risk of obscurity between a failure which is occurring in intermediate levels (referred to as a Fault) and one which is occurring finally (referred to as Failure).

## 2. Failure Rate

The reliability of a machine is its probability to perform its function within a defined period with certain restrictions under certain conditions. The reliability is the proportional expression of a machine's operational availability; therefore, it can be defined as the period when a machine can operate without any breakdowns. The equipment reliability depends to failures frequency, which is expressed by MTBF1 . Reliability predictions are based on failure rates. Failure intensity or λ(t)2 can be defined as "the foretasted number of times an item will break down in a determined time period, given that it was as good as new at time zero and is functioning at time t". This computed value provides a measurement of reliability for an equipment. This value is currently described as failures per million hours (f/mh). As an example, a component with a failure rate of 10 fpmh would be anticipated to fail 10 times for 1 million hours time period. The calculations of failure rate are based on complex models which include factors using specific component data such as stress, environment and temperature. In the prediction model,

1 Mean time between failures.

2 Conditional failure rate.

assembled components are organized serially. Thus, failure rates for assemblies are calculated by sum of the individual failure rates for components within the assembly. The MTBF was determined using Eq. (1). Failure rate which is equal to the reciprocal of the mean time between failures (MTBF) defined in hours (λ) was calculated by using Eq. (2) [1].

$$MTBF = \frac{T}{n} \tag{1}$$

$$
\lambda = \frac{1}{MTBF} \tag{2}
$$

3. Units

as failures per million (10�6

one billion (109

unit.

Any unit of time can be mentioned as failure rate unit, but hours is the most common unit in practice. Other units included miles, revolutions, etc., which can also replace the time units.

In engineering notation, failure rates are often very low because failure rates are often expressed

), particularly for individual components. The failures in time (FIT) rate for a component is the number of failures that can be occurred in

for each 1000 hours, or some other combination). Semiconductor industry currently used this

) use hours. (e.g., 1000 components for 1 million hours, or 1 million components

Failure Rate Analysis

103

http://dx.doi.org/10.5772/intechopen.71849

where, MTBF is mean time between failures, h; T is total time, h; n is number of failures; λ is failure rate, failures per 10n h.

There are some common basic categories of failure rates:

#### 2.1. Mean time between failures (MTBF)

The basic measure of reliability is mean time between failures (MTBF) for repairable equipment. MTBF can be expressed as the time passed before a component, assembly, or system break downs, under the condition of a constant failure rate. On the other hand, MTBF of repairable systems is the predicted value of time between two successive failures. It is a commonly used variable in reliability and maintainability analyses. MTBF can be calculated as the inverse of the failure rate, λ, for constant failure rate systems. For example, for a component with a failure rate of 2 failures per million hours, the MTBF would be the inverse of that failure rate, λ, or:

$$MTBF = \frac{1}{\lambda}$$

or

$$\frac{1}{2\pi f ailurər/10^6 \, həuurə} = 500\,000 \, hours \,/fatlurə$$

NOTE: Although MTBF was designed for use with repairable items, it is commonly used for both repairable and non-repairable items. For non-repairable items, MTBF is the time until the first (an only) failure after t0.

## 3. Units

assembled components are organized serially. Thus, failure rates for assemblies are calculated by sum of the individual failure rates for components within the assembly. The MTBF was determined using Eq. (1). Failure rate which is equal to the reciprocal of the mean time between

where, MTBF is mean time between failures, h; T is total time, h; n is number of failures; λ is

The basic measure of reliability is mean time between failures (MTBF) for repairable equipment. MTBF can be expressed as the time passed before a component, assembly, or system break downs, under the condition of a constant failure rate. On the other hand, MTBF of repairable systems is the predicted value of time between two successive failures. It is a commonly used variable in reliability and maintainability analyses. MTBF can be calculated as the inverse of the failure rate, λ, for constant failure rate systems. For example, for a component with a failure rate

NOTE: Although MTBF was designed for use with repairable items, it is commonly used for both repairable and non-repairable items. For non-repairable items, MTBF is

of 2 failures per million hours, the MTBF would be the inverse of that failure rate, λ, or:

ð1Þ

ð2Þ

failures (MTBF) defined in hours (λ) was calculated by using Eq. (2) [1].

There are some common basic categories of failure rates:

failure rate, failures per 10n h.

102 Failure Analysis and Prevention

• Mean Time Between Failures (MTBF)

• Probability of Failure on Demand (PFD)

2.1. Mean time between failures (MTBF)

the time until the first (an only) failure after t0.

• Mean Time To Failure (MTTF) • Mean Time To Repair (MTTR)

• Mean Down Time (MDT)

• Safety Integrity Level (SIL)

or

Any unit of time can be mentioned as failure rate unit, but hours is the most common unit in practice. Other units included miles, revolutions, etc., which can also replace the time units.

In engineering notation, failure rates are often very low because failure rates are often expressed as failures per million (10�6 ), particularly for individual components.

The failures in time (FIT) rate for a component is the number of failures that can be occurred in one billion (109 ) use hours. (e.g., 1000 components for 1 million hours, or 1 million components for each 1000 hours, or some other combination). Semiconductor industry currently used this unit.

Example 1 If we aim to estimate the failure rate of a certain component, we can carry out this test. Suppose each one of 10 same components are tested until they either break down or reach 1000 hours, after this time the test is completed for each component. The results are shown in Table 1 as follows:

, i.e., ~13.9% of these tractors may break down in the average year.

ð3Þ

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One of basic measures of reliability is mean time to failure (MTTF) for non-repairable systems. This statistical value is defined as the average time expected until the first failure of a component of equipment. MTTF is intended to be the mean over a long period of time and with a large number of units. For constant failure rate systems, MTTF can calculated by the failure rate inverse, 1/λ. Assuming failure rate, λ, be in terms of failures/million hours, MTTF =

For repairable systems, MTTF is the anticipated time period from repair to the first or next

Mean time to repair (MTTR) can described as the total time that spent to perform all corrective or preventative maintenance repairs divided by the total of repair numbers.  This is

Failure Density f(t)- The failure density of a component or system means that first failure what is likely to occur in the component or system at time t. In such cases, the component or system

Failure Rate or r(t)- The failure rate of a component or system is expressed as the probability per unit time that the component or system experiences a failure at time t. In such cases, the

Conditional failure rate or conditional failure intensity λ(t)– The conditional failure rate of a component or system is the probability per unit time that a failure occurs in the component or system at time t, so the component or system was operating, or was repaired to be as good as

Unconditional failure intensity or failure frequency ω(t)– The definition of the unconditional failure intensity of a component or system is the probability per unit time when the component or system fail at time t. In such cases, the component or system was using at time zero. The

1,000,000/failure rate, λ, for components with exponential distributions. Or:

3.1. Mean time to failure (MTTF)

3.2. Mean time to repair (MTTR)

was running at time zero.

a term that typically only used in repairable systems.

new, at time zero and is operating at time t.

Four failure frequencies are commonly used in reliability analyses:

component or system was using at time zero and has run to time t.

following relations (4) exist between failure parameters [2].

break down.

Table 1. Components failures during use hours.

Example 2 If a tractor be operated 24 hours a day, 7 days a week, so it will run 6540 hours for 1 year and at which time the MTBF number of a tractor be 1,050,000 hours:

; then the reciprocal of 160.55 years should be taken.

$$\frac{1\,\,failure}{160.55\,\, years} \times 100\,\% = 0.62\,\%$$

$$\boxed{\phantom}$$

In the average year, we can expect to fail about 0.62% of these tractors.

Example 3 Now assuming a tractor be operated at 6320 hours a year and at which time the MTBF number of this be 63,000 hours.

then the reciprocal of 9.968 years should be taken.

in the average year, we can expect to fail about 10.032% of these tractors.

You assume, we let the identical tractor run 24 hours a day, 7 days a week:

, i.e., ~13.9% of these tractors may break down in the average year.

#### 3.1. Mean time to failure (MTTF)

Example 1 If we aim to estimate the failure rate of a certain component, we can carry out this test. Suppose each one of 10 same components are tested until they either break down or reach 1000 hours, after this time the test is completed for each component. The results are shown in

Example 2 If a tractor be operated 24 hours a day, 7 days a week, so it will run 6540 hours for 1

Example 3 Now assuming a tractor be operated at 6320 hours a year and at which time the

; then the reciprocal of 160.55 years should be taken.

or 670 failures/million use hours.

then the reciprocal of 9.968 years should be taken.

in the average year, we can expect to fail about 10.032% of

year and at which time the MTBF number of a tractor be 1,050,000 hours:

Component Hours Failure 950 Failed 720 No failure 467 No failure 635 No failure 1000 Failed 602 No failure 1000 Failed 582 No failure 940 Failed 558 Failed Totals 7454 5

In the average year, we can expect to fail about 0.62% of these tractors.

You assume, we let the identical tractor run 24 hours a day, 7 days a week:

MTBF number of this be 63,000 hours.

Table 1. Components failures during use hours.

these tractors.

Table 1 as follows:

104 Failure Analysis and Prevention

One of basic measures of reliability is mean time to failure (MTTF) for non-repairable systems. This statistical value is defined as the average time expected until the first failure of a component of equipment. MTTF is intended to be the mean over a long period of time and with a large number of units. For constant failure rate systems, MTTF can calculated by the failure rate inverse, 1/λ. Assuming failure rate, λ, be in terms of failures/million hours, MTTF = 1,000,000/failure rate, λ, for components with exponential distributions. Or:

$$MTTF = \frac{1}{\lambda \, failures/10^6 hours} \tag{3}$$

For repairable systems, MTTF is the anticipated time period from repair to the first or next break down.

#### 3.2. Mean time to repair (MTTR)

Mean time to repair (MTTR) can described as the total time that spent to perform all corrective or preventative maintenance repairs divided by the total of repair numbers.  This is a term that typically only used in repairable systems.

Four failure frequencies are commonly used in reliability analyses:

Failure Density f(t)- The failure density of a component or system means that first failure what is likely to occur in the component or system at time t. In such cases, the component or system was running at time zero.

Failure Rate or r(t)- The failure rate of a component or system is expressed as the probability per unit time that the component or system experiences a failure at time t. In such cases, the component or system was using at time zero and has run to time t.

Conditional failure rate or conditional failure intensity λ(t)– The conditional failure rate of a component or system is the probability per unit time that a failure occurs in the component or system at time t, so the component or system was operating, or was repaired to be as good as new, at time zero and is operating at time t.

Unconditional failure intensity or failure frequency ω(t)– The definition of the unconditional failure intensity of a component or system is the probability per unit time when the component or system fail at time t. In such cases, the component or system was using at time zero. The following relations (4) exist between failure parameters [2].

$$R(t) + F(t) = 1\tag{4}$$

$$f(t) = \frac{dF(t)}{dt}$$

$$F(t) = \int\_0^t f(u) \, du$$

$$r(t) = \frac{f(t)}{1 - F(t)}$$

$$R(t) = e^{-\int\_0^t r(u) \, du}$$

$$f(t) = 1 - e^{-\int\_0^t r(u) \, du}$$

$$f(t) = r(t) \cdot e^{-\int\_t^t r(u) \, du}$$

self-imposed downtime, and any logistics or administrative delays. The MDT and MTTR (mean time to repair) are difference due to the MDT includes any and all delays involved; MTTR looks

Sometimes, Mean Time To Repair (MTTR) is used in this formula instead of MDT. But MTTR

If you used MDT or MTTR, it is important that it reflects the total time for which the equipment is unavailable for service, on the other hands the computed availability will be incorrect.

In the process industries, MTTR is often taken to be 8 hours, the length of a common work shift

PFD is probability of failure on demand. The design of safety systems are often such that to work in the background, monitoring a process, but not doing anything until a safety limit is overpassed when they must take some action to keep the process safe. These safety systems are

PFD means the unavailability of a safety task. If a demand to act occurs after a time, what is the probability that the safety function has already failed? As you might expect, the PFD equation

Note that we talk about PFDavg here, the mean probability of failure on demand, which is really the correct term to use, since the probability does change over time—the failure proba-

λDU is the failure rate of dangerous undetected failures. We are not counting any failures that are guessed to be "safe," perhaps because they cause the process to shut down, only those failures which remain hidden but will fail the operation of the safety function when it is called upon.

This is essential as it assures us not to suppose that a safety-related product is generally more reliable than a general purpose product. The aim of safety-related product design is to have especially low failure rate of the safety task, but its total failure rate (MTBF) may not be so efficient. So, the MDT for a safety function is defined as a dangerous undetected failure will not be

Suppose we proof test our safety function every year or two, say every T1 hours. The safety function is equally likely to fail at any time between one proof test and the next, so, on average

obvious until either a demand comes along or a proof test would be revealed it.

PFDavg ≈ λDU MDT (7)

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• Sometimes, the breakdown may not be considered after it has happened

• The equipment may not be put back in service immediately it is repaired

but the repair time really might be different particularly in an installation.

• The decision may be not to repair the equipment immediately

particularly at repair time.

may not be the identical as MDT because:

3.5. Probability of failure on demand (PFD)

often known as emergency shutdown (ESD) systems.

looks like the equation (7) for general unavailability [3]:

bility of a system will relied on how long ago you tested it.

it is down for T1/2 hours.

The difference between definitions for failure rate r(t) and conditional failure intensity λ(t) refers to first failure that the failure rate specifies this for the component or system rather than any failure of the component or system. Especially, if the failure rate being constant at considered time or if the component is non-repairable. These two quantities are same. So:

$$
\lambda(\mathbf{t}) = r(\mathbf{t}) \quad \text{for non-repairable components}
$$

$$
\lambda(\mathbf{t}) = r(\mathbf{t}) \quad \text{for constant failure rates}
$$

$$
\lambda(\mathbf{t}) \neq r(\mathbf{t}) \quad \text{for the general case}
$$

The conditional failure intensity (CFI) λ(t) and unconditional failure intensity ω(t) are different because the CFI has an additional condition that the component or system has survived to time t. The equation (5) mathematically showed the relationship between these two quantities.

$$
\lambda u(t) = \lambda(t)[1 - Q(t)]\tag{5}
$$

#### 3.3. Constant failure rates

If the failure rate is constant then the following expressions (6) apply:

$$\begin{aligned} R(t) &= \ e^{-\lambda t} \\ F(t) &= 1 - e^{-\lambda t} \\ f(t) &= \lambda .e^{-\lambda t} \end{aligned} \tag{6}$$

As can be seen from the equation above, a constant failure rate results in an exponential failure density distribution.

#### 3.4. Mean down time (MDT)

In organizational management, mean down time (MDT) is defined as the mean time that a system is not usable. This includes all time such as repair, corrective and preventive maintenance, self-imposed downtime, and any logistics or administrative delays. The MDT and MTTR (mean time to repair) are difference due to the MDT includes any and all delays involved; MTTR looks particularly at repair time.

Sometimes, Mean Time To Repair (MTTR) is used in this formula instead of MDT. But MTTR may not be the identical as MDT because:

If you used MDT or MTTR, it is important that it reflects the total time for which the equipment is unavailable for service, on the other hands the computed availability will be incorrect.

In the process industries, MTTR is often taken to be 8 hours, the length of a common work shift but the repair time really might be different particularly in an installation.

## 3.5. Probability of failure on demand (PFD)

ð4Þ

ð5Þ

ð6Þ

The difference between definitions for failure rate r(t) and conditional failure intensity λ(t) refers to first failure that the failure rate specifies this for the component or system rather than any failure of the component or system. Especially, if the failure rate being constant at consid-

The conditional failure intensity (CFI) λ(t) and unconditional failure intensity ω(t) are different because the CFI has an additional condition that the component or system has survived to time t. The equation (5) mathematically showed the relationship between these two

As can be seen from the equation above, a constant failure rate results in an exponential failure

In organizational management, mean down time (MDT) is defined as the mean time that a system is not usable. This includes all time such as repair, corrective and preventive maintenance,

ered time or if the component is non-repairable. These two quantities are same. So:

If the failure rate is constant then the following expressions (6) apply:

quantities.

106 Failure Analysis and Prevention

3.3. Constant failure rates

density distribution.

3.4. Mean down time (MDT)

PFD is probability of failure on demand. The design of safety systems are often such that to work in the background, monitoring a process, but not doing anything until a safety limit is overpassed when they must take some action to keep the process safe. These safety systems are often known as emergency shutdown (ESD) systems.

PFD means the unavailability of a safety task. If a demand to act occurs after a time, what is the probability that the safety function has already failed? As you might expect, the PFD equation looks like the equation (7) for general unavailability [3]:

$$\text{PFDavg} \approx \lambda\_{\text{DU}} \text{MDT} \tag{7}$$

Note that we talk about PFDavg here, the mean probability of failure on demand, which is really the correct term to use, since the probability does change over time—the failure probability of a system will relied on how long ago you tested it.

λDU is the failure rate of dangerous undetected failures. We are not counting any failures that are guessed to be "safe," perhaps because they cause the process to shut down, only those failures which remain hidden but will fail the operation of the safety function when it is called upon.

This is essential as it assures us not to suppose that a safety-related product is generally more reliable than a general purpose product. The aim of safety-related product design is to have especially low failure rate of the safety task, but its total failure rate (MTBF) may not be so efficient.

So, the MDT for a safety function is defined as a dangerous undetected failure will not be obvious until either a demand comes along or a proof test would be revealed it.

Suppose we proof test our safety function every year or two, say every T1 hours. The safety function is equally likely to fail at any time between one proof test and the next, so, on average it is down for T1/2 hours.

From this we get the simplest form of PFD calculation for safety functions [3]:

$$\text{PFDavg} \approx \text{\textquotedblleft} \lambda\_{\text{DU}} \text{ T}\_1 \tag{8}$$

failures. In the early life stage, failures as infant mortality often due to defects that escape the manufacturing process. In general, when the defective parts fail leaving a group of defect free products, the number of failures caused by manufacture problems decrease. Consequently the early stage failure rate decreases with age. During the useful life, failures may related to freak accidents and mishandling that subject the product to unexpected stress conditions. Suppose the failure rate over the useful life is generally very low and constant. As the equipment reaches to the wear-out stage, the degradation of equipment is related to repetitious or constant stress conditions. The failure rate during the wear-out stage increases dramatically as more and more occurs failure in equipment that caused by wear-out failures. When plotting the failure rate over time as illustrated in Figure 1, these stages make the so-called "bath tub"

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To ensure the integrity of design, we used many methods. Some of the design techniques include: burn-in (to stress devices under constant operating conditions); power cycling (to stress devices under the surges of turn-on and turn-off); temperature cycling (to mechanically and electrically stress devices over the temperature extremes); vibration; testing at the thermal destruct limits; highly accelerated stress and life testing; etc. Despite usage of all these design tools and manufacturing tools such as six sigma and quality improvement techniques, there will still be some early failures because we will not able to control processes at the molecular level. There is always the risk that, although the most up to date techniques are used in design and manufacture, early breakdowns will happen. In order to remove these risks — especially in newer product consumes some of the early useful life of a module via stress screening. The start of operating life in initial peak represents the highest risk of failure; since in this

curve.

4.1. Early life period

Figure 1. Bathtub curve for an ideal machine or component.

#### 3.6. SIL

Under reliability engineering, SIL is one of the most abused terms. "SIL" is often used to mention that an equipment or system show better quality, higher reliability, or some other desirable feature. It does not. SIL actually means safety integrity level and has a range between 1 and 4. It is applied to depict the safety protection degree required by a process and finally the safety reliability of the safety system is essential to obtain that protection. SIL4 shows the highest level of safety protection and SIL1 is the lowest.

Many products are demonstrated by "SIL" rated. This means that they are appropriate for use in safety systems. In fact, if this is true, it relies on a lot of detail, which is beyond the scope of this chapter. But remember that even when a product indeed matches with "SIL" needs that are only reminding you that it will do a definite job in a safety system. This safety reliability may be high, but its general reliability may not be, as mentioned in the prior section.

Useful to remember

## 4. Failure types

Failures generally be grouped into three basic types, though there may be more than one cause for a particular case. The three types included: early failures, random failures and wear-out failures. In the early life stage, failures as infant mortality often due to defects that escape the manufacturing process. In general, when the defective parts fail leaving a group of defect free products, the number of failures caused by manufacture problems decrease. Consequently the early stage failure rate decreases with age. During the useful life, failures may related to freak accidents and mishandling that subject the product to unexpected stress conditions. Suppose the failure rate over the useful life is generally very low and constant. As the equipment reaches to the wear-out stage, the degradation of equipment is related to repetitious or constant stress conditions. The failure rate during the wear-out stage increases dramatically as more and more occurs failure in equipment that caused by wear-out failures. When plotting the failure rate over time as illustrated in Figure 1, these stages make the so-called "bath tub" curve.

#### 4.1. Early life period

From this we get the simplest form of PFD calculation for safety functions [3]:

highest level of safety protection and SIL1 is the lowest.

service, it would be highly available.

performing a similar function.

Under reliability engineering, SIL is one of the most abused terms. "SIL" is often used to mention that an equipment or system show better quality, higher reliability, or some other desirable feature. It does not. SIL actually means safety integrity level and has a range between 1 and 4. It is applied to depict the safety protection degree required by a process and finally the safety reliability of the safety system is essential to obtain that protection. SIL4 shows the

Many products are demonstrated by "SIL" rated. This means that they are appropriate for use in safety systems. In fact, if this is true, it relies on a lot of detail, which is beyond the scope of this chapter. But remember that even when a product indeed matches with "SIL" needs that are only reminding you that it will do a definite job in a safety system. This safety reliability

• If an item works for a long time without breakdown, it can be said is highly reliable. • If an item does not fail very often and, when it does, it can be quickly returned to

• If a system is reliable in performing its safety function, it is considered to be safe. The system may fail much more frequently in modes that are not considered to be

• Finally, a safety system may be has lower MTBF in total than a non-safety system

• "SIL" does not mean a guarantee of quality or reliability, except in a defined safety

• MTBF is a measure of reliability, but it is not the expected life, the useful life, or the

• Calculations of reliability and failure rate of redundant systems are complex and

Failures generally be grouped into three basic types, though there may be more than one cause for a particular case. The three types included: early failures, random failures and wear-out

may be high, but its general reliability may not be, as mentioned in the prior section.

3.6. SIL

108 Failure Analysis and Prevention

Useful to remember

dangerous.

context.

4. Failure types

average life.

often counter-intuitive.

PFDavg ≈ ½ λDU T1 (8)

To ensure the integrity of design, we used many methods. Some of the design techniques include: burn-in (to stress devices under constant operating conditions); power cycling (to stress devices under the surges of turn-on and turn-off); temperature cycling (to mechanically and electrically stress devices over the temperature extremes); vibration; testing at the thermal destruct limits; highly accelerated stress and life testing; etc. Despite usage of all these design tools and manufacturing tools such as six sigma and quality improvement techniques, there will still be some early failures because we will not able to control processes at the molecular level. There is always the risk that, although the most up to date techniques are used in design and manufacture, early breakdowns will happen. In order to remove these risks — especially in newer product consumes some of the early useful life of a module via stress screening. The start of operating life in initial peak represents the highest risk of failure; since in this

Figure 1. Bathtub curve for an ideal machine or component.

technique, the units are allowed to begin their somewhere closer to the flat portion of the bathtub curve. Two factors included burn in and temperature cycling consumed the operating life. The amount of screening needed for acceptable quality is a function of the process grade as well as history. M-Grade modules are screened more than I-Grade modules, and I-Grade modules are screened more than C-Grade units.

4.5. Failure sources

Another categorization can be:

• Internal outage • External outage

4.6. Failure rate data

• Testing

4.7. Failure distribution types

There are two major categories for system outages: 1. Unplanned outages (failure) and 2. Planned outages (maintenance) that both conducted to downtime. In terms of cost, unplanned and planned outages are compared but use the redundant components maybe mitigate it. The planned outage usually has a sustainable impact on the system availability, if their schematization be appropriate. They are mostly happen due to maintenance. Some causes included periodic backup, changes in configuration, software upgrades and patches can caused by planned downtime. According to prior research studies 44% of downtime in service providers

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Specification and design flaws, manufacturing defects and wear-out categorized as internal factors. The radiation, electromagnetic interference, operator error and natural disasters can considered as external factors. However, a well-designed system or the components are highly reliable, the failures are unavoidable, but their impact mitigation on the system is possible.

Many organizations register the failure information of the equipment or systems that they produce, in which calculation of failure rates can be used for those devices or systems. For equipment or systems that produce recently, the historical data of similar equipment or

The available handbooks of failure rate data for various equipment can be obtained from government and commercial sources. MIL-HDBK-217F, reliability prediction of electrical equipment, is a military standard that provides failure rate data for many military electronic components. Several failure rate data sources are available commercially that focus

The most accurate source of data is to test samples of the actual devices or systems in order to generate failure data. This is often prohibitively expensive or impractical, so that

The different types of failure distribution are provided in Table 2. For an exponential failure distribution the hazard rate is a constant with respect to time (that is, the distribution is

on commercial components, including some non-electronic components.

The most common ways that failure rate data can be obtained as following:

• Historical data about the device or system under consideration.

systems can serve as a useful estimate.

• Government and commercial failure rate data.

the previous data sources are often used instead.

is unscheduled. This downtime period can spent lots of money.

## 4.2. Useful life period

The maturity of product is caused that the weaker units extinct, the failure rate nearly shows a constant trend, and modules have entered what is considered the normal life period. This period is characterized by a relatively constant failure rate. The length of this period is related to the product or component system life. During this period of time, the lowest failure rate happens. Notice how the amplitude on the bathtub curve is at its lowest during this time. The useful life period is the most common time frame for making reliability predictions.

## 4.3. MTBF vs. useful life

Sometimes MTBF is Mistakenly used instead of component's useful life. Consider, the useful life of a battery is 10 hours and the measure of MTBF is 100,000 hours. This means that in a set of 100,000 batteries, there will be about one battery failure every 1 hour during their useful lives.

Sometimes these numbers are so much high, it is related to the basis calculations of failure rate in usefulness period of component, and we suppose that the component will remain in this stage for a long period of time. In the above example, wear-out period decreases the component life, and the usefulness period becomes much smaller than its MTBF so there is not necessarily direct correlation between these two.

Consider another example, there are 15,000 18-year-old humans in the sample. Our investigation is related to 1 year. During this period, the death rate became 15/15,000 = 0.1%/year. The inverse of the failure rate or MTBF is 1/0.001 = 1000. This example represents that high MTBF values is different from the life expectancy. As people become older, more deaths occur, so the best way to calculate MTBF would be monitor the sample to reach their end of life. Then, the average of these life spans are computed. Then we approach to the order of 75–80 which would be very realistic.

#### 4.4. Wear-out period

As fatigue or wear-out occurs in components, failure rates increasing high. Power wear-out supplies is usually due to the electrical components breakdown that are subject to physical wear and electrical and thermal stress. Furthermore, the MTBFs or FIT rates calculated in the useful life period no longer apply in this area of the graph. A product with a MTBF of 10 years can still exhibit wear-out in 2 years. The wear-out time of components cannot predict by parts count method. Electronics in general, and Vicor power supplies in particular, are designed so that the useful life extends past the design life. This way wear-out should never occur during the useful life of a module.

#### 4.5. Failure sources

technique, the units are allowed to begin their somewhere closer to the flat portion of the bathtub curve. Two factors included burn in and temperature cycling consumed the operating life. The amount of screening needed for acceptable quality is a function of the process grade as well as history. M-Grade modules are screened more than I-Grade modules, and I-Grade

The maturity of product is caused that the weaker units extinct, the failure rate nearly shows a constant trend, and modules have entered what is considered the normal life period. This period is characterized by a relatively constant failure rate. The length of this period is related to the product or component system life. During this period of time, the lowest failure rate happens. Notice how the amplitude on the bathtub curve is at its lowest during this time. The

Sometimes MTBF is Mistakenly used instead of component's useful life. Consider, the useful life of a battery is 10 hours and the measure of MTBF is 100,000 hours. This means that in a set of 100,000 batteries, there will be about one battery failure every 1 hour during their useful

Sometimes these numbers are so much high, it is related to the basis calculations of failure rate in usefulness period of component, and we suppose that the component will remain in this stage for a long period of time. In the above example, wear-out period decreases the component life, and the usefulness period becomes much smaller than its MTBF so there is not

Consider another example, there are 15,000 18-year-old humans in the sample. Our investigation is related to 1 year. During this period, the death rate became 15/15,000 = 0.1%/year. The inverse of the failure rate or MTBF is 1/0.001 = 1000. This example represents that high MTBF values is different from the life expectancy. As people become older, more deaths occur, so the best way to calculate MTBF would be monitor the sample to reach their end of life. Then, the average of these life spans are computed. Then we approach to the order of 75–80 which

As fatigue or wear-out occurs in components, failure rates increasing high. Power wear-out supplies is usually due to the electrical components breakdown that are subject to physical wear and electrical and thermal stress. Furthermore, the MTBFs or FIT rates calculated in the useful life period no longer apply in this area of the graph. A product with a MTBF of 10 years can still exhibit wear-out in 2 years. The wear-out time of components cannot predict by parts count method. Electronics in general, and Vicor power supplies in particular, are designed so that the useful life extends past the design life. This way wear-out should never occur during

useful life period is the most common time frame for making reliability predictions.

modules are screened more than C-Grade units.

necessarily direct correlation between these two.

4.2. Useful life period

110 Failure Analysis and Prevention

4.3. MTBF vs. useful life

would be very realistic.

4.4. Wear-out period

the useful life of a module.

lives.

There are two major categories for system outages: 1. Unplanned outages (failure) and 2. Planned outages (maintenance) that both conducted to downtime. In terms of cost, unplanned and planned outages are compared but use the redundant components maybe mitigate it. The planned outage usually has a sustainable impact on the system availability, if their schematization be appropriate. They are mostly happen due to maintenance. Some causes included periodic backup, changes in configuration, software upgrades and patches can caused by planned downtime. According to prior research studies 44% of downtime in service providers is unscheduled. This downtime period can spent lots of money.

Another categorization can be:

Specification and design flaws, manufacturing defects and wear-out categorized as internal factors. The radiation, electromagnetic interference, operator error and natural disasters can considered as external factors. However, a well-designed system or the components are highly reliable, the failures are unavoidable, but their impact mitigation on the system is possible.

#### 4.6. Failure rate data

The most common ways that failure rate data can be obtained as following:

• Historical data about the device or system under consideration.

Many organizations register the failure information of the equipment or systems that they produce, in which calculation of failure rates can be used for those devices or systems. For equipment or systems that produce recently, the historical data of similar equipment or systems can serve as a useful estimate.

• Government and commercial failure rate data.

The available handbooks of failure rate data for various equipment can be obtained from government and commercial sources. MIL-HDBK-217F, reliability prediction of electrical equipment, is a military standard that provides failure rate data for many military electronic components. Several failure rate data sources are available commercially that focus on commercial components, including some non-electronic components.

• Testing

The most accurate source of data is to test samples of the actual devices or systems in order to generate failure data. This is often prohibitively expensive or impractical, so that the previous data sources are often used instead.

#### 4.7. Failure distribution types

The different types of failure distribution are provided in Table 2. For an exponential failure distribution the hazard rate is a constant with respect to time (that is, the distribution is

#### Distributions

Table 2. Failure distribution types.

"memoryless"). For other distributions, such as a Weibull distribution or a log-normal distribution, the hazard function is not constant with respect to time. For some such as the deterministic distribution it is monotonic increasing (analogous to "wearing out"), for others such as the Pareto distribution it is monotonic decreasing (analogous to "burning in"), while for many it is not monotonic.

#### 4.8. Derivations of failure rate equations for series and parallel systems

This section shows the derivations of the system failure rates for series and parallel configurations of constant failure rate components in Lambda Predict.

#### 4.9. Series system failure rate equations

Consider a system consisting of n components in series. For this configuration, the system reliability, Rs, is given by [4]:

$$R\_{\mathcal{S}} = \, \, R\_1. \, R\_2. \dots \, R\_n \tag{9}$$

It should be pointed out that if n blocks with non-constant (i.e., time-dependent) failure rates are arranged in a series configuration, then the system failure rate has a similar equation to the

Consider a system with n identical constant failure rate components arranged in a simple

where RC is the reliability of each component. Substituting the expression for component

Notice that this equation does not reduce to the form of a simple exponential distribution like for the case of a system of components arranged in series. In other words, the reliability of a system of constant failure rate components arranged in parallel cannot be modeled using a

To find the failure rate of a system of n components in parallel, the relationship between the reliability function, the probability density function and the failure rate is employed. The failure rate is defined as the ratio between the probability density and reliability functions, or:

Because the probability density function can be written in terms of the time derivative of the

parallel configuration. For this case, the system reliability equation is given by:

reliability in terms of the constant component failure rate, λC, yields:

ð13Þ

113

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ð14Þ

ð15Þ

ð16Þ

ð17Þ

ð18Þ

ð19Þ

one for constant failure rate blocks arranged in series and is given by:

4.10. Parallel system failure rate equations

constant system failure rate model.

and its time derivative is:

reliability function, the previous equation becomes:

The reliability of a system of n components in parallel is:

where R1, R2, …, Rn are the values of reliability for the n components. If the failure rates of the components are λ1, λ2,…, λn, then the system reliability is:

$$\begin{array}{rcl} R\_{\mathcal{S}} = & e^{-\lambda\_{\mathfrak{s}}\mathfrak{t}} . e^{-\lambda\_{\mathfrak{s}}\mathfrak{t}} . \dots , e^{-\lambda\_{\mathfrak{n}}\mathfrak{t}} \\ & = & e^{-(\lambda\_{\mathfrak{s}} + \lambda\_{\mathfrak{s}} + \dots + \lambda\_{\mathfrak{n}})\mathfrak{t}} \end{array} \tag{10}$$

Therefore, the system reliability can be expressed in terms of the system failure rate, λS, as:

$$R\_{\mathcal{S}} = \mathfrak{e}^{-\lambda\_{\mathfrak{g}}\mathfrak{t}} \tag{11}$$

Where and λS is constant. Note that since the component failure rates are constant, the system failure rate is constant as well. In other words, the system failure rate at any mission time is equal to the steady-state failure rate when constant failure rate components are arranged in a series configuration. If the components have identical failure rates, λC, then:

$$
\lambda\_{\mathfrak{s}} = n \lambda\_{\mathfrak{c}} \tag{12}
$$

It should be pointed out that if n blocks with non-constant (i.e., time-dependent) failure rates are arranged in a series configuration, then the system failure rate has a similar equation to the one for constant failure rate blocks arranged in series and is given by:

$$\lambda\_{\mathfrak{s}}(\mathfrak{t}) = \sum\_{i=1}^{n} \lambda\_i(\mathfrak{t}) \tag{13}$$

#### 4.10. Parallel system failure rate equations

"memoryless"). For other distributions, such as a Weibull distribution or a log-normal distribution, the hazard function is not constant with respect to time. For some such as the deterministic distribution it is monotonic increasing (analogous to "wearing out"), for others such as the Pareto distribution it is monotonic decreasing (analogous to "burning in"), while for

Weibull Covered

Extreme value Beyond the scope

Binomial Covered Normal Covered Poisson Covered Exponential Covered Multinomial Beyond the scope Lognormal Covered

This section shows the derivations of the system failure rates for series and parallel configura-

Consider a system consisting of n components in series. For this configuration, the system

where R1, R2, …, Rn are the values of reliability for the n components. If the failure rates of the

Therefore, the system reliability can be expressed in terms of the system failure rate, λS, as:

Where and λS is constant. Note that since the component failure rates are constant, the system failure rate is constant as well. In other words, the system failure rate at any mission time is equal to the steady-state failure rate when constant failure rate components are arranged in a series configuration. If the components have identical failure rates, λC, then:

ð9Þ

ð10Þ

ð11Þ

ð12Þ

4.8. Derivations of failure rate equations for series and parallel systems

tions of constant failure rate components in Lambda Predict.

Discrete Continuous

components are λ1, λ2,…, λn, then the system reliability is:

4.9. Series system failure rate equations

many it is not monotonic.

Table 2. Failure distribution types.

Distributions

112 Failure Analysis and Prevention

reliability, Rs, is given by [4]:

Consider a system with n identical constant failure rate components arranged in a simple parallel configuration. For this case, the system reliability equation is given by:

$$R\_{\varepsilon} = \mathbb{1} - (\mathbb{1} - R\_{\varepsilon})^n \tag{14}$$

where RC is the reliability of each component. Substituting the expression for component reliability in terms of the constant component failure rate, λC, yields:

$$R\_{\varepsilon} = 1 - (1 - e^{-\lambda\_{\mathbb{C}}\mathbb{E}})^n \tag{15}$$

Notice that this equation does not reduce to the form of a simple exponential distribution like for the case of a system of components arranged in series. In other words, the reliability of a system of constant failure rate components arranged in parallel cannot be modeled using a constant system failure rate model.

To find the failure rate of a system of n components in parallel, the relationship between the reliability function, the probability density function and the failure rate is employed. The failure rate is defined as the ratio between the probability density and reliability functions, or:

$$
\lambda\_x = \frac{f\_s}{R\_x} \tag{16}
$$

Because the probability density function can be written in terms of the time derivative of the reliability function, the previous equation becomes:

$$
\lambda\_s = \frac{-\frac{dR\_s}{dt}}{R\_x} \tag{17}
$$

The reliability of a system of n components in parallel is:

$$R\_{\varepsilon} = 1 - (1 - R\_{\varepsilon})^n \tag{18}$$

and its time derivative is:

$$\frac{dR\_s}{dt} = \ -n \left(1 - R\_c\right)^{n-1} \frac{dR\_c}{dt} \tag{19}$$

Substituting into the expression for the system failure rate yields:

$$\lambda\_s = \frac{-n\left(1 - R\_c\right)^{n-1}\frac{dR\_c}{dt}}{1 - (1 - R\_c)^n} \tag{20}$$

References

[1] Billinton R, Allan RN. Reliability Evaluation of Engineering Systems (Concepts and Tech-

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[2] Available from: http://www.reliabilityeducation.com/ReliabilityPredictionBasics.pdf

[4] Available from: http://www.weibull.com/hotwire/issue181/article181.htm

niques). New York, London: Plenum Press; 1992. 453 pp

[3] Available from: http://www.mtl-inst.com

For constant failure rate components, the system failure rate becomes:

$$\lambda\_x = \frac{n\lambda\_\varepsilon e^{-\lambda\_\varepsilon t} (1 - e^{-\lambda\_\varepsilon t})^{n-1}}{1 - (1 - e^{-\lambda\_\varepsilon t})^n} \tag{21}$$

Thus, the failure rate for identical constant failure rate components arranged in parallel is timedependent. Taking the limit of the system failure rate as t approaches infinity leads to the following expression for the steady-state system failure rate:

$$\begin{split} \lambda\_{s,today\,\,stateq} &= \lim\_{t \to \infty} \lambda\_s \\ \\ = \lim\_{t \to \infty} \frac{n\lambda\_c e^{-\lambda\_c t} (1 - e^{-\lambda\_c t})^{n-1}}{1 - (1 - e^{-\lambda\_c t})^n} \\ = n\lambda\_c \lim\_{t \to \infty} \frac{e^{-\lambda\_c t} (1 - e^{-\lambda\_c t})^{n-1}}{1 - (1 - e^{-\lambda\_c t})^n} \end{split} \tag{22}$$

Applying L'Hopital's rule one obtains:

$$
\lambda\_{\text{ssteedy stats}} = \ n \lambda\_{\sigma} \tag{23}
$$

So the steady-state failure rate for a system of constant failure rate components in a simple parallel arrangement is the failure rate of a single component. It can be shown that for a kout-of-n parallel configuration with identical components:

$$
\lambda\_{\text{astody state}} = \ n \lambda\_{\sigma} \tag{24}
$$

## Author details

Fatemeh Afsharnia

Address all correspondence to<EMAIL_ADDRESS>
Department of Biosystems Engineering, Ramin Agriculture and Natural Resources University of Khuzestan, Ahvaz, Khuzestan, Iran

## References

ð20Þ

ð21Þ

ð22Þ

ð23Þ

ð24Þ

Substituting into the expression for the system failure rate yields:

For constant failure rate components, the system failure rate becomes:

following expression for the steady-state system failure rate:

out-of-n parallel configuration with identical components:

Address all correspondence to<EMAIL_ADDRESS>
of Khuzestan, Ahvaz, Khuzestan, Iran

Applying L'Hopital's rule one obtains:

Author details

114 Failure Analysis and Prevention

Fatemeh Afsharnia

Thus, the failure rate for identical constant failure rate components arranged in parallel is timedependent. Taking the limit of the system failure rate as t approaches infinity leads to the

So the steady-state failure rate for a system of constant failure rate components in a simple parallel arrangement is the failure rate of a single component. It can be shown that for a k-

Department of Biosystems Engineering, Ramin Agriculture and Natural Resources University

**Chapter 8**

**Provisional chapter**

**General Perspectives on Seismic Retrofitting of**

**General Perspectives on Seismic Retrofitting of**

DOI: 10.5772/intechopen.69439

This chapter focuses on retrofitting of historical masonry structures from the point of seismic resistance based on failure analysis. In historical structures, restoration applications have become necessary because their life cycle of structural and nonstructural members is completed due to natural result of material structure, environmental conditions, and/ or user errors. One of the most important intervention decisions in restoration stages carried out in historical buildings is known as retrofitted of the structure. The choice techniques of retrofitting of the structural members are becoming a very important issue in the scope of restoration of historical masonry structures belonging to the cultural heritage. Additionally, it should be decided to optimally preserve such buildings' original forms and to make interventions to increase the building's service life; in this regard, it is important to preserve the structures' historical identity and constructional value. Therefore, retrofitting applications have become essential to prevent the damage level and to have adequate level of structural strength in order to resist dynamic effects such as earthquakes. In this chapter, it is aimed to determine the main principles by using conventional and modern techniques within the scope of laboratory tests and numerical approaches in

> © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

© 2017 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

and reproduction in any medium, provided the original work is properly cited.

With respect to ICOMOS 2001 document, a full understanding of the structural behavior and material characteristics is essential for any conservation and restoration project regarding the architectural heritage. It is suggested that the work of analysis and evaluation should be

**Keywords:** historical structures, retrofitting, numerical approach, visual inspection

**Historical Masonry Structures**

**Historical Masonry Structures**

Baris Sayin, Baris Yildizlar, Cemil Akcay and

Baris Sayin, Baris Yildizlar, Cemil Akcay and

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.69439

recovering the historical structures.

Tarik Serhat Bozkurt

**Abstract**

**1. Introduction**

Tarik Serhat Bozkurt

**Provisional chapter**

## **General Perspectives on Seismic Retrofitting of Historical Masonry Structures Historical Masonry Structures**

**General Perspectives on Seismic Retrofitting of**

DOI: 10.5772/intechopen.69439

Baris Sayin, Baris Yildizlar, Cemil Akcay and Tarik Serhat Bozkurt Tarik Serhat Bozkurt Additional information is available at the end of the chapter

Baris Sayin, Baris Yildizlar, Cemil Akcay and

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.69439

#### **Abstract**

This chapter focuses on retrofitting of historical masonry structures from the point of seismic resistance based on failure analysis. In historical structures, restoration applications have become necessary because their life cycle of structural and nonstructural members is completed due to natural result of material structure, environmental conditions, and/ or user errors. One of the most important intervention decisions in restoration stages carried out in historical buildings is known as retrofitted of the structure. The choice techniques of retrofitting of the structural members are becoming a very important issue in the scope of restoration of historical masonry structures belonging to the cultural heritage. Additionally, it should be decided to optimally preserve such buildings' original forms and to make interventions to increase the building's service life; in this regard, it is important to preserve the structures' historical identity and constructional value. Therefore, retrofitting applications have become essential to prevent the damage level and to have adequate level of structural strength in order to resist dynamic effects such as earthquakes. In this chapter, it is aimed to determine the main principles by using conventional and modern techniques within the scope of laboratory tests and numerical approaches in recovering the historical structures.

**Keywords:** historical structures, retrofitting, numerical approach, visual inspection

## **1. Introduction**

With respect to ICOMOS 2001 document, a full understanding of the structural behavior and material characteristics is essential for any conservation and restoration project regarding the architectural heritage. It is suggested that the work of analysis and evaluation should be

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2017 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

done with multidisciplinary approach, such as earthquake specialists, architects, engineers, and art historians. Additionally, it is considered necessary for these specialists to have common knowledge on the subject of conserving and upgrading or strengthening the historical structures [1].

includes: (i) collection of data and samples, (ii) preliminary examination, (iii) nondestructive inspection, (iv) mechanical testing, (v) selection and preservation of damaged surfaces, (vi) macroscopic and microscopic examination, (vii) preparation and examination of metallographic sections, (viii) damage classification, and (ix) report writing. In this chapter, the men-

General Perspectives on Seismic Retrofitting of Historical Masonry Structures

http://dx.doi.org/10.5772/intechopen.69439

119

One of the most important intervention decisions in restoration carried out in historical structures is retrofitting of the structure. Article 10 of the Venice Charter (1964) remarks that "Where traditional techniques prove inadequate, the consolidation of a monument can be achieved by the use of any modern technique for conservation and construction, the efficacy

Retrofitting applications in historical structures are performed in accordance with the intervention decisions based on conventional and modern techniques. The intervention solutions must rely on cost-benefit analyses and take into account their socioeconomic impact on society. An obvious requirement is to minimize as much as possible the disturbance of the owners of the building during the building rehabilitation. The financial resources available decisively influence the intervention solutions for the particular purposes, including labor work capacity, equipment, materials, duration of the work, etc. It is also compulsory to have alternative strategies for intervention and to evaluate the decrease in building vulnerability with various

The intervention strategy and the intervention techniques must take into account the following criteria: (i) seismic hazard level at the construction site, (ii) characteristics of the building's intended use (architectural constrains, original occupancy of the building, building structure, technical equipments within the building, etc.), (iii) building safety as a response to daily activities, mainly related to the seismic safety (structural vulnerability, vulnerability of nonstructural elements, appliances or/and equipments, building exposure or value, etc.), (iv) required level for building performance (life safeguarding, immediate occupancy after earthquake, preventing building collapse, etc.), (v) economic criteria, including insured and

reinsured value of the building, and (vi) technological capability available at the site.

As a rule, it is worth stating the preliminary consideration before the description of the retrofitting techniques. Once the technique is proposed, it should be experimentally studied to understand the best application procedure and also its effectiveness. Even so, no general repair and strengthening method exists due to variability of historical masonry structures in materials and construction techniques. On the contrary, methods are mostly determined

of which has been proven by scientific data and experience" [1].

tioned procedures are considered.

**3. Intervention strategies**

strategies [26].

**4. Retrofitting principles**

according to different masonry characteristics.

Masonry constructions in many countries worldwide are characterized by inadequate resistance to earthquakes loading. The use of appropriate techniques for retrofitting of historical masonry structures should be made by referencing to additional structural system and members as well as repair and retrofitting on period after built of the mentioned structures, and this fact is evaluated in terms of the protection of the original identity as well as the cultural value of the structures [2].

The preservation of the original form in the retrofitting applications of historical structures is taken into consideration and thus transferring building's historical identity to future generations may be possible. Besides that, the need for refunctioning of the structure, improvement of repair and strengthening techniques over time, technical specifications in force, and collaboration of experts of different disciplines leads to the development of new solutions in the restoration applications.

Repair and strengthening applications are commonly applied as part of restoration works of historical masonry structures for recent years [3–21]. Until 1980, the applied practices consist of removing floor arch or timber floor by preventing load-bearing masonry wall, building a secondary load-bearing system apart from the present bearing system by supplying a RC load-bearing system inside large internal spaces, and ruining architectural structure by joining columns and beams inside spaces.

In this study, seismic retrofitting applications in historical masonry structures are presented within the scope of laboratory tests and numerical analyses based on a cross-disciplinary study of civil engineering and architecture.

## **2. Failure analysis**

Structural failures and their investigation have become an active field of professional practice in which experts are retained to investigate the causes of failures, as well as to provide technical assistance to know the root cause. Failure need not always mean a structural collapses. It can make a structure deficient or dysfunctional in usage. It may even cause secondary adverse effects: (i) Safety failure (injury, death, or even risk to people), (ii) functional failure (compromise of intended usage), and (iii) ancillary failure (adverse effect on schedules, cost, or use) [22–24].

Failure analysis and prevention are significant parameters to all of the engineering disciplines. The materials engineer often plays a head role in the analysis of failures, whether a component or product fails in service or if failure occurs in manufacturing or during production processing. In all cases, one must determine the cause of failure to inhibit future occurrence, and/ or to increase the performance of the structure [25]. Generally, procedure for failure analysis includes: (i) collection of data and samples, (ii) preliminary examination, (iii) nondestructive inspection, (iv) mechanical testing, (v) selection and preservation of damaged surfaces, (vi) macroscopic and microscopic examination, (vii) preparation and examination of metallographic sections, (viii) damage classification, and (ix) report writing. In this chapter, the mentioned procedures are considered.

## **3. Intervention strategies**

done with multidisciplinary approach, such as earthquake specialists, architects, engineers, and art historians. Additionally, it is considered necessary for these specialists to have common knowledge on the subject of conserving and upgrading or strengthening the historical

Masonry constructions in many countries worldwide are characterized by inadequate resistance to earthquakes loading. The use of appropriate techniques for retrofitting of historical masonry structures should be made by referencing to additional structural system and members as well as repair and retrofitting on period after built of the mentioned structures, and this fact is evaluated in terms of the protection of the original identity as well as

The preservation of the original form in the retrofitting applications of historical structures is taken into consideration and thus transferring building's historical identity to future generations may be possible. Besides that, the need for refunctioning of the structure, improvement of repair and strengthening techniques over time, technical specifications in force, and collaboration of experts of different disciplines leads to the development of new solutions in the

Repair and strengthening applications are commonly applied as part of restoration works of historical masonry structures for recent years [3–21]. Until 1980, the applied practices consist of removing floor arch or timber floor by preventing load-bearing masonry wall, building a secondary load-bearing system apart from the present bearing system by supplying a RC load-bearing system inside large internal spaces, and ruining architectural structure by join-

In this study, seismic retrofitting applications in historical masonry structures are presented within the scope of laboratory tests and numerical analyses based on a cross-disciplinary

Structural failures and their investigation have become an active field of professional practice in which experts are retained to investigate the causes of failures, as well as to provide technical assistance to know the root cause. Failure need not always mean a structural collapses. It can make a structure deficient or dysfunctional in usage. It may even cause secondary adverse effects: (i) Safety failure (injury, death, or even risk to people), (ii) functional failure (compromise of intended usage), and (iii) ancillary failure (adverse effect on schedules, cost, or use)

Failure analysis and prevention are significant parameters to all of the engineering disciplines. The materials engineer often plays a head role in the analysis of failures, whether a component or product fails in service or if failure occurs in manufacturing or during production processing. In all cases, one must determine the cause of failure to inhibit future occurrence, and/ or to increase the performance of the structure [25]. Generally, procedure for failure analysis

structures [1].

118 Failure Analysis and Prevention

the cultural value of the structures [2].

ing columns and beams inside spaces.

study of civil engineering and architecture.

restoration applications.

**2. Failure analysis**

[22–24].

One of the most important intervention decisions in restoration carried out in historical structures is retrofitting of the structure. Article 10 of the Venice Charter (1964) remarks that "Where traditional techniques prove inadequate, the consolidation of a monument can be achieved by the use of any modern technique for conservation and construction, the efficacy of which has been proven by scientific data and experience" [1].

Retrofitting applications in historical structures are performed in accordance with the intervention decisions based on conventional and modern techniques. The intervention solutions must rely on cost-benefit analyses and take into account their socioeconomic impact on society. An obvious requirement is to minimize as much as possible the disturbance of the owners of the building during the building rehabilitation. The financial resources available decisively influence the intervention solutions for the particular purposes, including labor work capacity, equipment, materials, duration of the work, etc. It is also compulsory to have alternative strategies for intervention and to evaluate the decrease in building vulnerability with various strategies [26].

The intervention strategy and the intervention techniques must take into account the following criteria: (i) seismic hazard level at the construction site, (ii) characteristics of the building's intended use (architectural constrains, original occupancy of the building, building structure, technical equipments within the building, etc.), (iii) building safety as a response to daily activities, mainly related to the seismic safety (structural vulnerability, vulnerability of nonstructural elements, appliances or/and equipments, building exposure or value, etc.), (iv) required level for building performance (life safeguarding, immediate occupancy after earthquake, preventing building collapse, etc.), (v) economic criteria, including insured and reinsured value of the building, and (vi) technological capability available at the site.

## **4. Retrofitting principles**

As a rule, it is worth stating the preliminary consideration before the description of the retrofitting techniques. Once the technique is proposed, it should be experimentally studied to understand the best application procedure and also its effectiveness. Even so, no general repair and strengthening method exists due to variability of historical masonry structures in materials and construction techniques. On the contrary, methods are mostly determined according to different masonry characteristics.

Appropriate site and laboratory investigations should always be carried out before reinforcement application through: (i) an accurate geometrical survey of the structure's morphology; (ii) characterization of the constituent materials, e.g., stones and of the mortars in masonry structures; (iii) survey of the physical and mechanical decay; and (iv) crack pattern survey. Based on these considerations, it is possible to choose between several systems of retrofitting and application techniques.

The seismic retrofitting methods can be classified as follows, as far as their target is concerned: **a.** In case the target is the increase of stiffness and structural strength, the most effective method is the addition of walls in the existing frames. What follows is the method of adding truss bracings, the method of adding walls as an extension of existing columns, and the

General Perspectives on Seismic Retrofitting of Historical Masonry Structures

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121

**b.** In case the target is the increase of plasticity, the method that is recommended is the application of jacketing on a number of selected columns, as well as the use of composite

**c.** In case the target is the simultaneous increase of strength, stiffness, and plasticity of the structure, any seismic strengthening method can be used taking into consideration the required degree of increasing each of the above-mentioned characteristics. In case that the necessary increases are very high for all the three characteristics, the addition of new verti-

Within the scope of examined masonry structures, in order to determine structural changing or the construction time of an examined structure, it should be investigated whether or not the structure is in place using ancient maps. In the stage of the restoration project, historical photos and old maps are utilized in collecting data and documents on the building facade; therefore, information on floor height, storey count, roof patio, roof form of the structure, relationship with the neighboring structures, and location of the windows is obtained.

The current state of an examined structure must be defined within the context of the structural and nonstructural members and the position in the plane must be given. Threedimensional (3D) laser scanning method should be used to determine the geometric dimensions and structural damage of the structure in detail. Then, the structural supplements in the historical process of examined structure must be presented in detail. Thus, the differences between the first period and the current situation of an examined structure will be

Samples are gathered from various points of a structure during laboratory test phase of the study and after then analyses are performed. Thereby, axial compressive strength of the masonry walls, shear strength, bulk density, and thick- and thin-plaster compounds are derived. Moreover, mechanical characteristics of bricks and pointing fillings are

use of composite materials.

cal members is generally inevitable.

**5.1. Historical process of the structures**

**5.2. Existing status of the structures**

clarified.

**5.3. Field study**

determined.

**5. Structural evaluation of masonry structures**

materials.

Three important preservation principles should be kept in mind when undertaking seismic retrofit projects: [26]

While seismic upgrading work is often more permanent than reversible, care must be taken to preserve historical materials to the historical appearance of the building.

In addition to the above principles, the general aim of structure conservation is to preserve the cultural significance of the place where the building is culturally aggregated. Places of cultural significance should be safeguarded and not left at risk in a vulnerable state.

The different intervention works are defined in various manners and documents from various countries, as well as in general literature. The relationship between the stages for seismic rehabilitation of historical buildings is presented in **Figure 1**.

**Figure 1.** Value alteration diagram of a building [26].

The seismic retrofitting methods can be classified as follows, as far as their target is concerned:

## **5. Structural evaluation of masonry structures**

#### **5.1. Historical process of the structures**

Within the scope of examined masonry structures, in order to determine structural changing or the construction time of an examined structure, it should be investigated whether or not the structure is in place using ancient maps. In the stage of the restoration project, historical photos and old maps are utilized in collecting data and documents on the building facade; therefore, information on floor height, storey count, roof patio, roof form of the structure, relationship with the neighboring structures, and location of the windows is obtained.

#### **5.2. Existing status of the structures**

The current state of an examined structure must be defined within the context of the structural and nonstructural members and the position in the plane must be given. Threedimensional (3D) laser scanning method should be used to determine the geometric dimensions and structural damage of the structure in detail. Then, the structural supplements in the historical process of examined structure must be presented in detail. Thus, the differences between the first period and the current situation of an examined structure will be clarified.

#### **5.3. Field study**

Appropriate site and laboratory investigations should always be carried out before reinforcement application through: (i) an accurate geometrical survey of the structure's morphology; (ii) characterization of the constituent materials, e.g., stones and of the mortars in masonry structures; (iii) survey of the physical and mechanical decay; and (iv) crack pattern survey. Based on these considerations, it is possible to choose between several systems of retrofitting

Three important preservation principles should be kept in mind when undertaking seismic

• Historical materials should be preserved at the largest extent possible and not replaced

• New seismic retrofit systems, whether hidden or exposed, should respect and should be

• Seismic work should be "reversible" to the largest extent possible to allow future removal

While seismic upgrading work is often more permanent than reversible, care must be taken to

In addition to the above principles, the general aim of structure conservation is to preserve the cultural significance of the place where the building is culturally aggregated. Places of

The different intervention works are defined in various manners and documents from various countries, as well as in general literature. The relationship between the stages for seismic

cultural significance should be safeguarded and not left at risk in a vulnerable state.

compatible to the architectural and structural integrity of the historical structure.

wholly with other new materials in the process of seismic strengthening.

preserve historical materials to the historical appearance of the building.

rehabilitation of historical buildings is presented in **Figure 1**.

and application techniques.

for the use of future improved systems.

**Figure 1.** Value alteration diagram of a building [26].

retrofit projects: [26]

120 Failure Analysis and Prevention

Samples are gathered from various points of a structure during laboratory test phase of the study and after then analyses are performed. Thereby, axial compressive strength of the masonry walls, shear strength, bulk density, and thick- and thin-plaster compounds are derived. Moreover, mechanical characteristics of bricks and pointing fillings are determined.

## *5.3.1. Shear strength of walls in situ*

Shear strength index of brick-mortar in masonry walls are defined based upon shear tests which are performed in different points in the structure in relation to standard. Samples are compressive strength and bulk density tests are performed on such samples—taken representing the brick-mortar-brick system—in the laboratory.

corresponding to the 12 modes are calculated for an examined structure in modal analysis. The period values are found out for x- and y-directions. For each earthquake direction in the regulations [27], shear stresses on the walls are attained by rating the horizontal force coming to the horizontal load-bearing members to horizontal section area of masonry walls. After that, calculated values are compared to the experimental shear stress ones. Shear stresses of all walls in both directions of a masonry structure are determined to be adequate to cover the

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123

FE analysis of a multistorey masonry structure under seismic loading is performed. Wall shear strength to be used in numerical analyses is determined individually for each of the storey. The structural performances are determined based on the existing building's loadbearing data obtained by using linear elastic analyses. According to the analyses, principles defined as per related country's local provisions and standards, all analyses are carried out using a general purpose FE software [28, 29]. In terms of evaluation of the existing structures, the structure is analyzed considering four different building performance levels for the existing or strengthened buildings, in addition to various level earthquake definitions. The performance levels are specified as: (a) operational, (b) immediate occupancy, (c) life safety, and (d)

Building performance can be defined qualitatively from the point of: (i) safety afforded building occupants, during and after an earthquake; (ii) cost and feasibility of restoring the building to preearthquake circumstances; (iii) length of time the building is removed from service to conduct repairs; and (iv) economical, architectural, or historical effects on the community in general. These performance properties will be squarely related to the extent of damage

In the numerical analyses performed under a described earthquake design, it is specified that the existing system meets the conditions set forth for life safety performance level. For an earthquake with 10% recovery possibility in 50 years, it is determined that the shear strength of all the walls in both directions of the masonry building is ordinarily adequate to

**Figure 2.** Levels of building performance: (a) operational, (b) immediate occupancy, (c) life-safety, and (d) collapse

shear stresses under earthquake effects.

collapse prevention or near collapse (**Figure 2**).

sustained by the building during an earthquake.

*5.5.1. Structural model*

prevention [30].

## *5.3.2. Mechanical and physical properties of mortars and brick samples*

Samples from the solid brick blocks and pointing filling mortars are gathered from an examined structure. Single-axis compressive strength and bulk density tests are performed on brick blocks. For the purpose of determining the dead weight of the wall, density of filling mortars between the bricks is considered.

## *5.3.3. Elastic modulus of walls*

In consequence of the tests performed on an examined structure, in parallel with the data and previous experiences acquired from other masonry structures having comparable historical process, construction conditions, and materials, it is decided that the elastic modulus, taking into consideration the condition of the existing walls, can be used on the structural model.

#### **5.4. Laboratory analysis**

As a laboratory study, physical test and chemical analysis are carried out on samples taken from a historical building. Subsequently, the proposal mixtures of plaster and mortar for restoration are determined according to the laboratory test results. The locations of samples from the masonry ruin are determined. Properties and detailed visual definition of the provided samples are obtained. Then, samples are taken from different points of the examined structure during lab test stage of the study and analyses are carried out. The samples are exposed to chemical, physical, and mineralogical tests, such as the ratio of binders, aggregates, and mineralogical compositions, and textural properties of the mortar samples are analyzed, and the cause for deteriorations is determined by visual analysis, spot tests analysis, ignition loss analysis, reaction with acid, and petrography. Before starting the analyzes, it is examined that the texture, color, state (integrity) of the samples; color, size, approximate quantities, apparent organic additives and type of aggregates in the contents of the samples. After that, the size distribution, particle properties of acid insoluble materials, and protein/ oil contents are determined. Samples taken are examined by content analysis within the scope of related standards along with visual detailing. Consequently, axial compressive strength of the masonry walls, shear strength, bulk density, and thick and thin plaster compounds are obtained. Also, mechanical characteristics of bricks and pointing fillings are obtained.

## **5.5. Numerical analysis**

In the numerical analysis carried out with general purpose, finite element analysis software, period values, modal participation mass ratios, and total modal participation mass ratios corresponding to the 12 modes are calculated for an examined structure in modal analysis. The period values are found out for x- and y-directions. For each earthquake direction in the regulations [27], shear stresses on the walls are attained by rating the horizontal force coming to the horizontal load-bearing members to horizontal section area of masonry walls. After that, calculated values are compared to the experimental shear stress ones. Shear stresses of all walls in both directions of a masonry structure are determined to be adequate to cover the shear stresses under earthquake effects.

#### *5.5.1. Structural model*

*5.3.1. Shear strength of walls in situ*

122 Failure Analysis and Prevention

mortars between the bricks is considered.

*5.3.3. Elastic modulus of walls*

**5.4. Laboratory analysis**

**5.5. Numerical analysis**

senting the brick-mortar-brick system—in the laboratory.

characteristics of bricks and pointing fillings are obtained.

*5.3.2. Mechanical and physical properties of mortars and brick samples*

Shear strength index of brick-mortar in masonry walls are defined based upon shear tests which are performed in different points in the structure in relation to standard. Samples are compressive strength and bulk density tests are performed on such samples—taken repre-

Samples from the solid brick blocks and pointing filling mortars are gathered from an examined structure. Single-axis compressive strength and bulk density tests are performed on brick blocks. For the purpose of determining the dead weight of the wall, density of filling

In consequence of the tests performed on an examined structure, in parallel with the data and previous experiences acquired from other masonry structures having comparable historical process, construction conditions, and materials, it is decided that the elastic modulus, taking into consideration the condition of the existing walls, can be used on the structural model.

As a laboratory study, physical test and chemical analysis are carried out on samples taken from a historical building. Subsequently, the proposal mixtures of plaster and mortar for restoration are determined according to the laboratory test results. The locations of samples from the masonry ruin are determined. Properties and detailed visual definition of the provided samples are obtained. Then, samples are taken from different points of the examined structure during lab test stage of the study and analyses are carried out. The samples are exposed to chemical, physical, and mineralogical tests, such as the ratio of binders, aggregates, and mineralogical compositions, and textural properties of the mortar samples are analyzed, and the cause for deteriorations is determined by visual analysis, spot tests analysis, ignition loss analysis, reaction with acid, and petrography. Before starting the analyzes, it is examined that the texture, color, state (integrity) of the samples; color, size, approximate quantities, apparent organic additives and type of aggregates in the contents of the samples. After that, the size distribution, particle properties of acid insoluble materials, and protein/ oil contents are determined. Samples taken are examined by content analysis within the scope of related standards along with visual detailing. Consequently, axial compressive strength of the masonry walls, shear strength, bulk density, and thick and thin plaster compounds are obtained. Also, mechanical

In the numerical analysis carried out with general purpose, finite element analysis software, period values, modal participation mass ratios, and total modal participation mass ratios FE analysis of a multistorey masonry structure under seismic loading is performed. Wall shear strength to be used in numerical analyses is determined individually for each of the storey. The structural performances are determined based on the existing building's loadbearing data obtained by using linear elastic analyses. According to the analyses, principles defined as per related country's local provisions and standards, all analyses are carried out using a general purpose FE software [28, 29]. In terms of evaluation of the existing structures, the structure is analyzed considering four different building performance levels for the existing or strengthened buildings, in addition to various level earthquake definitions. The performance levels are specified as: (a) operational, (b) immediate occupancy, (c) life safety, and (d) collapse prevention or near collapse (**Figure 2**).

Building performance can be defined qualitatively from the point of: (i) safety afforded building occupants, during and after an earthquake; (ii) cost and feasibility of restoring the building to preearthquake circumstances; (iii) length of time the building is removed from service to conduct repairs; and (iv) economical, architectural, or historical effects on the community in general. These performance properties will be squarely related to the extent of damage sustained by the building during an earthquake.

In the numerical analyses performed under a described earthquake design, it is specified that the existing system meets the conditions set forth for life safety performance level. For an earthquake with 10% recovery possibility in 50 years, it is determined that the shear strength of all the walls in both directions of the masonry building is ordinarily adequate to

**Figure 2.** Levels of building performance: (a) operational, (b) immediate occupancy, (c) life-safety, and (d) collapse prevention [30].

meet the shear forces occurring under the subject to earthquake effects. In that case, it can be underlined that a structure meets that "immediate usage performance level"; however, due to insufficiencies not meeting a masonry structure definitions of the structure and partially determined irregularities, "life safety performance level" should be used to evaluate, rather than "immediate usage performance level."

*<IP_ADDRESS>. Checking of shear stress in walls*

and design.

exhaustive.

**6.1. Retrofitting of masonry walls**

Shear stresses on the walls are obtained by proportioning the horizontal force coming to the horizontal load-bearing members to horizontal section area of masonry wall for each earthquake direction in the earthquake provision. Calculated values are compared to the experimental shear stress values. Shear stresses are calculated individually for each storey and wall across building height. Total shear force is calculated for FE analysis for each direction by proportioning the total section area in that direction, and principal stress comparisons are

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Storey shear forces obtained from analysis are compared to the forces that are experimentally obtained and shear stress checking is carried out in the structure. Shear performance on *x*- and *y*-directions is presented. Shear strength of all the walls in both directions of the masonry building is determined to be adequate to cover the shear forces under earthquake effects. Also, it is checked whether the checking meet the rules for the structure geometry

In the retrofitting stage of the structures, plaster analyses and mechanical tests are conducted on the samples taken from the examined structure. After that, the structure's existing 3D computer model is prepared and members that are inadequate in terms of strength are determined. Within the scope of the analysis, it is found that the structure can be converted to the original form of the structure. In this regard, featureless additions, which are not related to the original structure, are removed and restoration applications are carried out. In the scope of restoration applications, structural cracks on the walls are repaired using the injection method. Moreover, jack-arched floor, exterior facade walls, interior walls, and door/window

As a cross-disciplinary study must be carried out in the strengthening stage of the historical building, improved or changed details are manufactured with the approval of engineering and architecture disciplines. Retrofitting applications include: (i) walls, (ii) jack-arched floors (volta slabs), (iii) door and window gaps, and (iv) foundations. In this section, retrofitting applications illustrating the effectiveness of the described method will be presented. It should be noted that the presented applications are for example only and are not intended to be

In an examined structure, it is decided that masonry walls will be strengthened removing plastering on masonry walls, detection of structural cracks and strengthening using the method of injection in accordance with supervisor decisions regarding strengthening masonry walls.

made on the shell elements together with shear stress for each storey.

**6. The retrofitting applications of masonry structures**

*6.1.1. Retrofitting of cracks in masonry walls using injection technique*

gaps using different techniques are strengthened.

Building performance levels typically comprise a structural performance level that describes the limiting damage state of the structural systems, plus a nonstructural performance level that describes the limiting damage state of the nonstructural systems and components. A structure examined by using mode combination method is calculated under earthquake loads; all acceptances and obtained values are determined in accordance with the Turkish Earthquake Regulation. A three-dimensional model of an examined structure is prepared. In the prepared model walls and slabs that are horizontal structural members are modeled as shell element in the element library of the FE analysis software. Mechanical properties of the structural members in the model are transferred to the structural system via the data obtained from the experimental studies mentioned above.

## *5.5.2. Analysis of structures*

#### *<IP_ADDRESS>. Compliance with earthquake regulation*

In determining the structure's performance, controls are made based on local or international earthquake regulations [26]. A three-dimensional linear finite element analysis of examined multistorey masonry structure under seismic loading is carried out.

The following checks should be evaluated in accordance with seismic regulation:

Based on the regulation, supported walls in masonry structures should be as regular and arranged as a symmetrically or close to symmetric, and construction of local basement should be avoided. The structure is examined considering these criteria and it is determined whether the structure is regular or not on the plan.

#### *<IP_ADDRESS>. Modal analysis*

Twelve modes are calculated for the building in modal analysis and period values corresponding to the modes are presented. Participation mass ratio and period values are examined and the vertical and horizontal period values are obtained. Data presented demonstrate that which direction is more rigid than the other direction.

## *<IP_ADDRESS>. Checking of shear stress in walls*

meet the shear forces occurring under the subject to earthquake effects. In that case, it can be underlined that a structure meets that "immediate usage performance level"; however, due to insufficiencies not meeting a masonry structure definitions of the structure and partially determined irregularities, "life safety performance level" should be used to evaluate, rather

Building performance levels typically comprise a structural performance level that describes the limiting damage state of the structural systems, plus a nonstructural performance level that describes the limiting damage state of the nonstructural systems and components. A structure examined by using mode combination method is calculated under earthquake loads; all acceptances and obtained values are determined in accordance with the Turkish Earthquake Regulation. A three-dimensional model of an examined structure is prepared. In the prepared model walls and slabs that are horizontal structural members are modeled as shell element in the element library of the FE analysis software. Mechanical properties of the structural members in the model are transferred to the structural system via the data obtained

In determining the structure's performance, controls are made based on local or international earthquake regulations [26]. A three-dimensional linear finite element analysis of examined

• Nonsupported length between the vertically connected masonry wall axes to the plane of

Based on the regulation, supported walls in masonry structures should be as regular and arranged as a symmetrically or close to symmetric, and construction of local basement should be avoided. The structure is examined considering these criteria and it is determined whether

Twelve modes are calculated for the building in modal analysis and period values corresponding to the modes are presented. Participation mass ratio and period values are examined and the vertical and horizontal period values are obtained. Data presented demonstrate

multistorey masonry structure under seismic loading is carried out.

any masonry wall is checked in according to earthquake zone

• The height of each storey should be checked in masonry buildings

• Control of the total maximum length of the masonry walls

• Limit conditions in door and window gaps in the walls

that which direction is more rigid than the other direction.

the structure is regular or not on the plan.

*<IP_ADDRESS>. Modal analysis*

The following checks should be evaluated in accordance with seismic regulation:

than "immediate usage performance level."

from the experimental studies mentioned above.

*<IP_ADDRESS>. Compliance with earthquake regulation*

*5.5.2. Analysis of structures*

124 Failure Analysis and Prevention

Shear stresses on the walls are obtained by proportioning the horizontal force coming to the horizontal load-bearing members to horizontal section area of masonry wall for each earthquake direction in the earthquake provision. Calculated values are compared to the experimental shear stress values. Shear stresses are calculated individually for each storey and wall across building height. Total shear force is calculated for FE analysis for each direction by proportioning the total section area in that direction, and principal stress comparisons are made on the shell elements together with shear stress for each storey.

Storey shear forces obtained from analysis are compared to the forces that are experimentally obtained and shear stress checking is carried out in the structure. Shear performance on *x*- and *y*-directions is presented. Shear strength of all the walls in both directions of the masonry building is determined to be adequate to cover the shear forces under earthquake effects. Also, it is checked whether the checking meet the rules for the structure geometry and design.

## **6. The retrofitting applications of masonry structures**

In the retrofitting stage of the structures, plaster analyses and mechanical tests are conducted on the samples taken from the examined structure. After that, the structure's existing 3D computer model is prepared and members that are inadequate in terms of strength are determined. Within the scope of the analysis, it is found that the structure can be converted to the original form of the structure. In this regard, featureless additions, which are not related to the original structure, are removed and restoration applications are carried out. In the scope of restoration applications, structural cracks on the walls are repaired using the injection method. Moreover, jack-arched floor, exterior facade walls, interior walls, and door/window gaps using different techniques are strengthened.

As a cross-disciplinary study must be carried out in the strengthening stage of the historical building, improved or changed details are manufactured with the approval of engineering and architecture disciplines. Retrofitting applications include: (i) walls, (ii) jack-arched floors (volta slabs), (iii) door and window gaps, and (iv) foundations. In this section, retrofitting applications illustrating the effectiveness of the described method will be presented. It should be noted that the presented applications are for example only and are not intended to be exhaustive.

#### **6.1. Retrofitting of masonry walls**

#### *6.1.1. Retrofitting of cracks in masonry walls using injection technique*

In an examined structure, it is decided that masonry walls will be strengthened removing plastering on masonry walls, detection of structural cracks and strengthening using the method of injection in accordance with supervisor decisions regarding strengthening masonry walls. It is aimed to increase the bearing capacity of masonry walls using injection method, as filling the structural slots inside the masonry walls with lime binder injection mortar.

Following completing plaster removal on all masonry walls, structural cracks are determined. Repair mixture ratios are determined based on the gathered samples, and the mixtures are prepared. The mixture is applied to the cracks by means of manual injection. Integration is ensured using steel clamp members in larger cracks and anchorage elements on the walls are anchored via epoxy.

As it takes time to settle the injection compound into the wall, application is repeated periodically. The compound inside the pipe is penetrated into the interior walls in time, the pipes are continuously injected, and this process is continued until the gaps are filled. **Figure 3** shows possible injection application in the walls.

## *6.1.2. Retrofitting of masonry walls in-plane using carbon fiber wrap*

Carbon fiber wrap can be used in tensile stress areas on wall members to strength dynamic effects, e.g., earthquake. First, applied carbon fiber locations are specified on the facades. Carbon fiber wrap is positioned between window gaps and storey levels and also disguised under plaster layer. **Figure 4** shows possible carbon fiber application in the walls.

*6.1.3. Retrofitting of internal walls using rebar grids technique*

**Figure 4.** Carbon fiber wrap applications on masonry walls (a and b).

drilled on masonry walls and filled with epoxy (**Figure 5**).

plaster.

After having completed the existing plaster removal from the vertical load-carrying members, internal wall strengthening is applied. In this respect, anchorage holes per square meter are

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**Figure 5.** Retrofitting of the internal walls after plaster removal: (a–c) rebar grid technique and (d) application of thick

**Figure 3.** Injection application in the walls after plaster removal: (a) structural cracks, (b) preparation of wall surface for injection, and (c) injection application by manual technique.

**Figure 4.** Carbon fiber wrap applications on masonry walls (a and b).

It is aimed to increase the bearing capacity of masonry walls using injection method, as filling

Following completing plaster removal on all masonry walls, structural cracks are determined. Repair mixture ratios are determined based on the gathered samples, and the mixtures are prepared. The mixture is applied to the cracks by means of manual injection. Integration is ensured using steel clamp members in larger cracks and anchorage elements on the walls

As it takes time to settle the injection compound into the wall, application is repeated periodically. The compound inside the pipe is penetrated into the interior walls in time, the pipes are continuously injected, and this process is continued until the gaps are filled.

Carbon fiber wrap can be used in tensile stress areas on wall members to strength dynamic effects, e.g., earthquake. First, applied carbon fiber locations are specified on the facades. Carbon fiber wrap is positioned between window gaps and storey levels and also disguised

**Figure 3.** Injection application in the walls after plaster removal: (a) structural cracks, (b) preparation of wall surface for

injection, and (c) injection application by manual technique.

under plaster layer. **Figure 4** shows possible carbon fiber application in the walls.

the structural slots inside the masonry walls with lime binder injection mortar.

**Figure 3** shows possible injection application in the walls.

*6.1.2. Retrofitting of masonry walls in-plane using carbon fiber wrap*

are anchored via epoxy.

126 Failure Analysis and Prevention

## *6.1.3. Retrofitting of internal walls using rebar grids technique*

After having completed the existing plaster removal from the vertical load-carrying members, internal wall strengthening is applied. In this respect, anchorage holes per square meter are drilled on masonry walls and filled with epoxy (**Figure 5**).

**Figure 5.** Retrofitting of the internal walls after plaster removal: (a–c) rebar grid technique and (d) application of thick plaster.

## **6.2. Retrofitting of jack-arched floors**

Floor system strengthening consists of two separate parts: (i) Strengthening without removing jack-arched floors, which are positioned on the hallways and assumed as the original ones and (ii) applications of steel beam system installation is applied with the aim of lighting the weight of the building as removing featureless RC additions. **Figure 6** presents a similar application about floor strengthening.

**6.4. Retrofitting of foundations**

**Figure 8.** Retrofitting of foundations in masonry structures.

**Figure 7.** Retrofitting of door and window gaps using steel plates (a and b).

For foundation strengthening, it is managed that all masonry walls are to move together by tying them with each other with bond beams and RC foundations and also aimed to transfer

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