A technology-dependent issue is, whether irradiation is carried out in bulk or in sealed packages of the finished product. Bioactive compounds are anticipated to decompose less in the latter case, although radiolysis products, involatile or volatile, may diffuse into the product from the packaging material [27]. Reduced amounts of carotenoids were reported at high irradiation dosages and long storage (e.g., 11.1 and 42.1% decrease in capsanthin levels upon irradiation at 10 kGy and a subsequent 10-month storage period, respectively) [28]. Approximately 40% reduction in anti-oxidant activity was seen upon a 20-week storage period, compared to 13% decrease in the control non-irradiated ground black pepper [29].

#### **7.2. Steam treatment**

and mould contamination increased by two orders of magnitude. This is due to the fact that the microbial load of paprika berries is not homogenous; a few heavily spoiled ones mixed with the healthy berries can contaminate the entire product (**Figure 2C**). The chemical composition,

**Figure 2.** The effect of technology steps on the microbial status of the paprika half-product. **A**: slicing, **B**: drying,

Another CCP in the technology chain is at the microbial decontamination. To enhance food safety of spice paprika, a decontamination step needs to be carried out to secure the microbial purity of the product and to avoid contamination of food seasoned with it [17]. Various methods are in use and are incorporated into the processing technology (generally after the grinding step) or available for decontamination [18]. Their efficiency in reducing the microbial load in dried spices has been evaluated in literature [19]. Nonetheless, even though red sweet paprika is appreciated being an excellent source of essential nutrients and bioactive compounds, these assessments generally do not evaluate the effects the decontamination step may exert on the

Microbial decontamination is most often carried out by steam treatment or by irradiation by ionising radiation (e.g., gamma irradiation—the maximum allowed average radiation dose being 10 kGy) [20]. In spite of the high efficacy of microbial decontamination by irradiation, and even though legal regulations allow (and even advise) this technology in the EU for decontamination of dried herbs and spices, producers tend to choose steam treatment due to consumer aversion from the food radiation technology [21]. Consumer acceptance of irradiation remains poor despite numerous efforts of food industry experts and the EU legislation to dispel misconceptions regarding the use of isotope techniques and ionising radiation [22]. It has to be also mentioned, that sensory and anti-oxidative properties of the finished product may be slightly affected by the technology used [23]. Irradiation (at 1, 5 and 10 kGy doses) was proven highly effective in the treatment of ground dry spice paprika: the aerobic mesophilic total count (log) decreased from 6.84 to 5.08, 4.71 and 2.91 log cfu/g, respectively, while the

however, did not appear to undergo any significant change.

composition of the bioactive, aroma and colour components.

**paprika**

**C**: grinding.

**7.1. Irradiation treatment**

**7. Effects of the decontamination steps on the quality of spice**

124 Quality Management Systems - a Selective Presentation of Case-studies Showcasing Its Evolution

Steaming is a decontamination technique of spices of proven and high utility. Due to steam treatment (saturated dry steam, 108 –125°C for 20–120 s) the mesophilic aerobic total bacterial count from 1.8 × 105 cfu/g to 6.0 × 102 cfu/g and moulds from 1.3 × 102 cfu/g to under the detection limit were reduced, while yeasts, coliforms, *E. coli* and *Enterobacteriaceae* could not be detected. According to the molecular identification, the dominant bacteria were spore forming rods, family *Bacillaceae,* namely *B. methylotrophicus, B. pumilus, B. vallismortis* and *B. sonorensis* before, while *B. methylotrophicus, B. pumilus* and *B. amyloliquefaciens* after treatment. The concentration of the main bioactive compounds, as capsanthin esters, total carotenoids, tocopherols, vitamin C and the ASTA value did not change significantly, however, the total tocopherol content decreased by 6%. The area percentage (%) of the volatile aroma compounds (e.g., acetic acid and pentanal) decreased, while in some cases (e.g., geranyl acetone, β-ionone and dihydroactinidiolide) a slight increase was detected.

Steam treatment was shown to cause a reduction of volatile oil content along with discoloration [30], and although high-temperature steaming is effective against contaminating microorganisms, it can decrease the volatile oil content, cause colour degradation and may increase the moisture content of dried paprika product, which then reduces shelf-life [31]. Furthermore, steaming is not suitable for spore inactivation. These results confirm that steaming provides a good possibility to reduce the microbial load, without drastically changing the content of bioactive compounds.

bioactive components and on the texture of spice paprika [35]. Pasteurisation treatment at high hydrostatic pressure (500 MPa) had less influence on the bioactive component content

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Chemical treatment with ethylene oxide is also a worldwide available decontamination technology, but the potential use is limited by its toxicity. Due to its carcinogenic potential to humans, the use of ethylene oxide is forbidden to be used in food processing in the EU [36].

As mentioned above, the last one among the three CCPs within the spice paprika processing technology is at the mixing step, where the imported half-products get into the manufacturing process. Determination of the origin or ensuring the authenticity of red paprika products is of high importance from both food safety and commercial aspects. To assess the composition of bioactive ingredients in spice paprika and to support the safety of the spice product chains, a wide range of compositional examinations were performed on spice paprika sam-

A method of combining strontium isotope ratios with a multi-element pattern by means of inductively coupled plasma mass spectrometry (ICP-MS) was used to create a unique fingerprint of authentic Szegedi Fűszerpaprika and to categorise authentic and purchased paprika from different known, declared and unknown geographical origins, using principal component and canonical discriminant analysis [37]. Changes in element and strontium isotopic composition (87Sr/86Sr ratio) were examined throughout the production process. As such, the geographical origin of the spice paprika can be determined even after processing. Strontium isotope ratios are combined with multi-element pattern analysis in the "fingerprint" method, using ICP-MS, and another proper indicator of cultivation types (agrochemicals) and geographical origin (e.g., a distinction between Asia and Europe) is the δ15N value. A clear distinction between Japanese and foreign paprika products was achieved on the basis of their Cu and Rb content by ICP-MS [38]. Similarly, sweet, hot and hot/sweet paprika samples from Spain were assessed by their micro-elemental composition by ICP-MS followed by chemometric classmodelling techniques on variables selected by stepwise linear discriminant analysis [39, 40].

Origin-protected Spanish spice paprika samples (Murcia and Extremadura) were analysed by colour characteristics to differentiate between geographical origins [41]. Co-ordinates in the CIELAB colour space and ASTA scale were measured from acetone extracts of paprika samples in UV-Vis spectral range. For origin discrimination multi-layer perceptrons, artificial neural networks models presented the best results for all types of paprika. According to another strategy [42], the entire absorbance range from 380 to 780 nm was used, and data was combined and reduced by means of principal component analysis. The anti-oxidant activity and the composition of polyphenolics and carbohydrates of spice paprika (Lakošnička and Lemeška) were investigated to attempt to verify the regional and botanical origin of Serbian autochthonous clones of red spice paprika using multi-variate statistical methods [43]. In addition, distinction was achieved to be made between Dutch bell peppers and those from

and on the texture, than at low pressure.

**8. The effect of the geographical origin**

ples of several geographical origins.

#### **7.3. Microwave and enhanced microwave heating**

Even though well-described and evaluated industrial decontamination processes are available, alternative methods are also being developed and investigated for efficacy and effects. Microwave heating is advocated for effective reduction of the level of mesophilic bacteria. The method (98°C for 20 min) was indicated to reduce the total number of mesophilic bacteria 6.3\*104 -fold [32]. Microwave heating (30 s in dry and wet treatment) was found to allow the highest reduction of the bacterial level in chilli among different spices studied [33]. It is worth noting at this point that the method (100 s at various temperatures) did not result in a relevant reduction of the total counts of mesophilic aerobic bacteria even at 95°C, but affected the colour of the treated paprika lot unfavourably, giving it a darker, brownish character.

To avoid the detrimental effect of the treatment method on the colour of spice paprika, a modified microwave treatment (including re-wetting of the sample, intensive mixing during the entire treatment and post-drying to the initial moisture level) was also evaluated by the authors. Mesophilic aerobic total bacterial counts were not significantly affected by the enhanced microwave treatment, however, mould populations and coliforms were reduced, if samples were kept at the given temperatures for at least 10 min. Significant changes were detected in carotenoids, and total tocopherol content decreased by 6.2% only at higher initial moisture content (30% and higher, 10 min, 95°C). Thus, enhanced microwave treatment allows a reduction of microbial contamination (principally for moulds and coliforms) without a decrease in the levels of bioactive compounds. The temperature did not significantly affect chemical composition, but had a significant effect on sample colour.

Nonetheless, in spite the corrected moisture content, all samples became browner and darker after the treatment, and as colour changes did not correlate with the observed levels in carotenoids and the ASTA value, it has been concluded that colour changes due to the treatment are likely to be related to plant carbohydrates and proteins.

#### **7.4. Other treatments**

Oregano essential oil was attempted as a natural anti-microbial agent to reduce microbial count in paprika [34]. Although it was not found to be of adequate activity by itself to allow sufficient inactivation of microbial spores in paprika, when used in combination with highpressure carbon dioxide, microbial inactivation largely increased (by 99.5%).

In a number of food products, high hydrostatic pressures increase shelf-life and maintain nutritional and organoleptic properties better, the effect of high hydrostatic pressures and pasteurisation (in a water bath at 70°C for 10 min) was examined on the levels of given bioactive components and on the texture of spice paprika [35]. Pasteurisation treatment at high hydrostatic pressure (500 MPa) had less influence on the bioactive component content and on the texture, than at low pressure.

Chemical treatment with ethylene oxide is also a worldwide available decontamination technology, but the potential use is limited by its toxicity. Due to its carcinogenic potential to humans, the use of ethylene oxide is forbidden to be used in food processing in the EU [36].

## **8. The effect of the geographical origin**

Steam treatment was shown to cause a reduction of volatile oil content along with discoloration [30], and although high-temperature steaming is effective against contaminating microorganisms, it can decrease the volatile oil content, cause colour degradation and may increase the moisture content of dried paprika product, which then reduces shelf-life [31]. Furthermore, steaming is not suitable for spore inactivation. These results confirm that steaming provides a good possibility to reduce the microbial load, without drastically changing the

126 Quality Management Systems - a Selective Presentation of Case-studies Showcasing Its Evolution

Even though well-described and evaluated industrial decontamination processes are available, alternative methods are also being developed and investigated for efficacy and effects. Microwave heating is advocated for effective reduction of the level of mesophilic bacteria. The method (98°C for 20 min) was indicated to reduce the total number of mesophilic bacteria

colour of the treated paprika lot unfavourably, giving it a darker, brownish character.

chemical composition, but had a significant effect on sample colour.

are likely to be related to plant carbohydrates and proteins.

**7.4. Other treatments**

To avoid the detrimental effect of the treatment method on the colour of spice paprika, a modified microwave treatment (including re-wetting of the sample, intensive mixing during the entire treatment and post-drying to the initial moisture level) was also evaluated by the authors. Mesophilic aerobic total bacterial counts were not significantly affected by the enhanced microwave treatment, however, mould populations and coliforms were reduced, if samples were kept at the given temperatures for at least 10 min. Significant changes were detected in carotenoids, and total tocopherol content decreased by 6.2% only at higher initial moisture content (30% and higher, 10 min, 95°C). Thus, enhanced microwave treatment allows a reduction of microbial contamination (principally for moulds and coliforms) without a decrease in the levels of bioactive compounds. The temperature did not significantly affect

Nonetheless, in spite the corrected moisture content, all samples became browner and darker after the treatment, and as colour changes did not correlate with the observed levels in carotenoids and the ASTA value, it has been concluded that colour changes due to the treatment

Oregano essential oil was attempted as a natural anti-microbial agent to reduce microbial count in paprika [34]. Although it was not found to be of adequate activity by itself to allow sufficient inactivation of microbial spores in paprika, when used in combination with high-

In a number of food products, high hydrostatic pressures increase shelf-life and maintain nutritional and organoleptic properties better, the effect of high hydrostatic pressures and pasteurisation (in a water bath at 70°C for 10 min) was examined on the levels of given

pressure carbon dioxide, microbial inactivation largely increased (by 99.5%).

content of bioactive compounds.

6.3\*104

**7.3. Microwave and enhanced microwave heating**

As mentioned above, the last one among the three CCPs within the spice paprika processing technology is at the mixing step, where the imported half-products get into the manufacturing process. Determination of the origin or ensuring the authenticity of red paprika products is of high importance from both food safety and commercial aspects. To assess the composition of bioactive ingredients in spice paprika and to support the safety of the spice product chains, a wide range of compositional examinations were performed on spice paprika samples of several geographical origins.

A method of combining strontium isotope ratios with a multi-element pattern by means of inductively coupled plasma mass spectrometry (ICP-MS) was used to create a unique fingerprint of authentic Szegedi Fűszerpaprika and to categorise authentic and purchased paprika from different known, declared and unknown geographical origins, using principal component and canonical discriminant analysis [37]. Changes in element and strontium isotopic composition (87Sr/86Sr ratio) were examined throughout the production process. As such, the geographical origin of the spice paprika can be determined even after processing. Strontium isotope ratios are combined with multi-element pattern analysis in the "fingerprint" method, using ICP-MS, and another proper indicator of cultivation types (agrochemicals) and geographical origin (e.g., a distinction between Asia and Europe) is the δ15N value. A clear distinction between Japanese and foreign paprika products was achieved on the basis of their Cu and Rb content by ICP-MS [38]. Similarly, sweet, hot and hot/sweet paprika samples from Spain were assessed by their micro-elemental composition by ICP-MS followed by chemometric classmodelling techniques on variables selected by stepwise linear discriminant analysis [39, 40].

Origin-protected Spanish spice paprika samples (Murcia and Extremadura) were analysed by colour characteristics to differentiate between geographical origins [41]. Co-ordinates in the CIELAB colour space and ASTA scale were measured from acetone extracts of paprika samples in UV-Vis spectral range. For origin discrimination multi-layer perceptrons, artificial neural networks models presented the best results for all types of paprika. According to another strategy [42], the entire absorbance range from 380 to 780 nm was used, and data was combined and reduced by means of principal component analysis. The anti-oxidant activity and the composition of polyphenolics and carbohydrates of spice paprika (Lakošnička and Lemeška) were investigated to attempt to verify the regional and botanical origin of Serbian autochthonous clones of red spice paprika using multi-variate statistical methods [43]. In addition, distinction was achieved to be made between Dutch bell peppers and those from other countries, using analytical strategies based on bulk δ18O elemental analysis of source and paprika fruit water, and on compound-specific, n-alkane, δ2H gas chromatography coupled to isotope ratio mass spectrometry analysis [44].

**10. Conclusion**

**Acknowledgements**

**Author details**

Szandra Klátyik1

András Székács1

Proper quality control measures at each of the above steps along with effective interaction between producers' quality management practices and government activities are key factors in the provision of environmental and food safety of spice paprika production. To illustrate this, quality assurance measures established along spice paprika production technologies are surveyed with main CCPs identified. Concerted performance of internal (manufacturer) and external (state) quality control measures act in synergy to guarantee good production practice

Quality Management in Spice Paprika Production: From Cultivation to End Product

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129

This work was supported by EU-project SPICED (Grant Agreement: 312631) with the financial support from the 7th Framework Programme of the European Union and by projects OTKA K109865 and K112978 by the Hungarian Scientific Research Fund. This publication reflects the views only of the authors, and the European Commission cannot be held responsible for any

, Ildikó Bata-Vidács1

, Nóra Adányi2

and

and to support product quality in spice paprika cultivation and processing.

, Miklós Pék3

1 Agro-Environmental Research Institute, National Agricultural Research and Innovation

2 Food Science Research Institute, National Agricultural Research and Innovation Centre,

3 Vegetable Crop Research Department, National Agricultural Research and Innovation

[1] Lakner Z, Szabó E, Szűcs V, Székács A. Network and vulnerability analysis of international

[2] Valle-Algarra MF, Mateo ME, Mateo R, Gimeno-Adelantado VJ, Jiménez M. Determination of type A and type B trichothecenes in paprika and chili pepper using LC-triple quadrupole-MS and GC-ECD. Talanta. 2011;**84**:1112-1117. DOI: 10.1016/j.

spice trade. Food Control. 2018;**83**:141-146. DOI: 10.1016/j.foodcont.2017.05.042

use which may be made of the information contained therein.

, Helga Molnár2

\*Address all correspondence to<EMAIL_ADDRESS>
\*

Centre, Budapest, Hungary

Centre, Kalocsa, Hungary

talanta.2011.03.017

Budapest, Hungary

**References**

Gas chromatography-olfactometry was also applied for the evaluation and identification of the odour-active compounds combined with the flavour dilution (FD) factors [45]. For the control of aflatoxin B1 and total aflatoxins in spice paprika powder, NIRS technique as an alternative method was applied using the Modified Partial Least Squares (MPLS) algorithm as a regression method [46]. Moreover, the contamination of mycotoxins (e.g., fumonisin B1, ochratoxin A and sterigmatocystin) and pesticide residues (e.g. metalaxyl fungicide) in spices were investigated by ultra-high performance liquid chromatography (UHPLC) coupled to a high resolution Orbitrap mass spectrometry (Orbitrap-HRMS) [47].

To identify major differences in characteristics and chemical component composition of spice paprika by their origin, a set of samples (53 pieces) was investigated [48]. Samples from Spain and Peru showed outstandingly high total carotenoids content (in average 3709 and 3810 μg/g, respectively), and the ratio of capsanthin diesters to free capsanthins was found to be a good indicator of origin, supposedly due to differing climate conditions in the two countries. The calculated capsanthin diesters/free capsanthins ratio was found to be in average 4.0, 5.3, 8.1, 8.2, 17.1 and 22.0 in samples from Serbia, Hungary, Spain, Bulgaria, China and Peru, respectively. According to the results of NIR evaluation of spice paprika samples, there occurred some clustering among the samples according the country of origin.

The geographical origin of spice paprika has also been successfully attempted to be characterised by their dominant microflora [49]. Although no substantial differences were found among the microbial loads of spice paprika samples from different countries (Brazil, Bulgaria, China, Hungary, India, Kenya, Peru, Serbia, Spain, Thailand and unknown origin) on the EU market, bacterial species in the dominant microflora, characteristic to climate, were identified. The presence of *B. mycoides* and *B. licheniformis* were found to be characteristic to Central Europe, *B. mojavensis* to Spain, *B. safensis* to tropical monsoon climate, *B. amyloliquefaciens* subsp. *plantarum* and *B. amyloliquefaciens* subsp. *amyloliquefaciens* to tropical climate, and no common species was identified for China.

### **9. Internal and external quality control measures**

In addition to obligatory quality control and assurance measures by the producers and systematic analysis for compliance with food safety requirements at EU community level by RASFF, national authorities in EU member states also perform external control analyses to assure food safety (EC Regulation No 882/2004). At present, there are no microbiological criteria for dried spices in the European Community legislation, although, the Codex Code of Hygienic Practice specifies that dried spices should be free of pathogenic microorganisms at levels that may represent a health hazard. The European Spice Association (ESA) and the European Commission (EC) Recommendation 2004/24/EC specify that *Salmonella* spp. should be absent in 25 g of spice, *E. coli* must be under 102 cfu/g, and other bacteria requirements should be agreed between the buyer and the seller [50].

## **10. Conclusion**

other countries, using analytical strategies based on bulk δ18O elemental analysis of source and paprika fruit water, and on compound-specific, n-alkane, δ2H gas chromatography cou-

Gas chromatography-olfactometry was also applied for the evaluation and identification of the odour-active compounds combined with the flavour dilution (FD) factors [45]. For the control of aflatoxin B1 and total aflatoxins in spice paprika powder, NIRS technique as an alternative method was applied using the Modified Partial Least Squares (MPLS) algorithm as a regression method [46]. Moreover, the contamination of mycotoxins (e.g., fumonisin B1, ochratoxin A and sterigmatocystin) and pesticide residues (e.g. metalaxyl fungicide) in spices were investigated by ultra-high performance liquid chromatography (UHPLC) coupled to a

To identify major differences in characteristics and chemical component composition of spice paprika by their origin, a set of samples (53 pieces) was investigated [48]. Samples from Spain and Peru showed outstandingly high total carotenoids content (in average 3709 and 3810 μg/g, respectively), and the ratio of capsanthin diesters to free capsanthins was found to be a good indicator of origin, supposedly due to differing climate conditions in the two countries. The calculated capsanthin diesters/free capsanthins ratio was found to be in average 4.0, 5.3, 8.1, 8.2, 17.1 and 22.0 in samples from Serbia, Hungary, Spain, Bulgaria, China and Peru, respectively. According to the results of NIR evaluation of spice paprika samples, there

The geographical origin of spice paprika has also been successfully attempted to be characterised by their dominant microflora [49]. Although no substantial differences were found among the microbial loads of spice paprika samples from different countries (Brazil, Bulgaria, China, Hungary, India, Kenya, Peru, Serbia, Spain, Thailand and unknown origin) on the EU market, bacterial species in the dominant microflora, characteristic to climate, were identified. The presence of *B. mycoides* and *B. licheniformis* were found to be characteristic to Central Europe, *B. mojavensis* to Spain, *B. safensis* to tropical monsoon climate, *B. amyloliquefaciens* subsp. *plantarum* and *B. amyloliquefaciens* subsp. *amyloliquefaciens* to tropical climate, and no

In addition to obligatory quality control and assurance measures by the producers and systematic analysis for compliance with food safety requirements at EU community level by RASFF, national authorities in EU member states also perform external control analyses to assure food safety (EC Regulation No 882/2004). At present, there are no microbiological criteria for dried spices in the European Community legislation, although, the Codex Code of Hygienic Practice specifies that dried spices should be free of pathogenic microorganisms at levels that may represent a health hazard. The European Spice Association (ESA) and the European Commission (EC) Recommendation 2004/24/EC specify that *Salmonella* spp. should be absent in 25 g of spice, *E. coli* must be under 102 cfu/g, and other bacteria require-

pled to isotope ratio mass spectrometry analysis [44].

common species was identified for China.

**9. Internal and external quality control measures**

ments should be agreed between the buyer and the seller [50].

high resolution Orbitrap mass spectrometry (Orbitrap-HRMS) [47].

128 Quality Management Systems - a Selective Presentation of Case-studies Showcasing Its Evolution

occurred some clustering among the samples according the country of origin.

Proper quality control measures at each of the above steps along with effective interaction between producers' quality management practices and government activities are key factors in the provision of environmental and food safety of spice paprika production. To illustrate this, quality assurance measures established along spice paprika production technologies are surveyed with main CCPs identified. Concerted performance of internal (manufacturer) and external (state) quality control measures act in synergy to guarantee good production practice and to support product quality in spice paprika cultivation and processing.

## **Acknowledgements**

This work was supported by EU-project SPICED (Grant Agreement: 312631) with the financial support from the 7th Framework Programme of the European Union and by projects OTKA K109865 and K112978 by the Hungarian Scientific Research Fund. This publication reflects the views only of the authors, and the European Commission cannot be held responsible for any use which may be made of the information contained therein.

## **Author details**

Szandra Klátyik1 , Helga Molnár2 , Miklós Pék3 , Ildikó Bata-Vidács1 , Nóra Adányi2 and András Székács1 \*

\*Address all correspondence to<EMAIL_ADDRESS>
1 Agro-Environmental Research Institute, National Agricultural Research and Innovation Centre, Budapest, Hungary

2 Food Science Research Institute, National Agricultural Research and Innovation Centre, Budapest, Hungary

3 Vegetable Crop Research Department, National Agricultural Research and Innovation Centre, Kalocsa, Hungary

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**Chapter 7**

Provisional chapter

**Adaptive CUSUM for Steady State Normal Data**

DOI: 10.5772/intechopen.70752

This chapter deals with monitoring plans that exploit temporal predictable trends by adjusting the cumulative sum (CUSUM) plan to be efficient for their early detection. The adjustment involves changing the amount of memory the chart retains to detect persistent changes in location early. The focus is on steady-state situations when either the shift size is known in advance or when it is unknown. Several options are explored

Keywords: average run length, early detection, monitoring, persistent trends, statistical

The adaptive CUSUM of Sparks [12] exploits temporal predictable trends by adjusting its design to be efficient for the early detection of such trends. The adjustment involves changing

In the zero-state case, Moustakides [6] proved that a step change of δ is best detected by using Page's [7] conventional CUSUM with the reference value k = δ/2. Gan [3] demonstrated that the conventional CUSUM with k = 0.5 is optimal in the zero-state in their Table 1 for a shift of one and standard normal distributed data. The adaptive CUSUM has been shown to be better at times at detecting small shifts in location than the conventional CUSUM with the optimal k value for that shift. For example, in the standard normal distribution case, the shift of 1 for the adaptive CUSUM is detected with an average run length (ARL); in Table 3 of Sparks [12] is 9.29 or 9.34, while the zero state optimal conventional CUSUM with k = 0.5 has an ARL of 9.34 (see also [5] Table 2). Hence, the adaptive CUSUM can have smaller out-of-control ARLs than the best CUSUM in the zero-state situation. The reason for this is that, for smaller shifts, the adaptive CUSUM can exploit the steady-state situation by making use of the local knowledge about the size of its shift. For unknown large shifts this is more difficult because one often flags the change before it can be accurately predicted. In other words the adaptive CUSUM

> © 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.

© 2018 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.

the amount of memory the chart retains to detect persistent changes in location earlier.

using simulation studies, and an example of application is considered.

Adaptive CUSUM for Steady State Normal Data

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.70752

Ross Sparks

Ross Sparks

Abstract

process control

1. Introduction

#### **Adaptive CUSUM for Steady State Normal Data** Adaptive CUSUM for Steady State Normal Data

DOI: 10.5772/intechopen.70752

#### Ross Sparks Ross Sparks

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.70752

#### Abstract

This chapter deals with monitoring plans that exploit temporal predictable trends by adjusting the cumulative sum (CUSUM) plan to be efficient for their early detection. The adjustment involves changing the amount of memory the chart retains to detect persistent changes in location early. The focus is on steady-state situations when either the shift size is known in advance or when it is unknown. Several options are explored using simulation studies, and an example of application is considered.

Keywords: average run length, early detection, monitoring, persistent trends, statistical process control

## 1. Introduction

The adaptive CUSUM of Sparks [12] exploits temporal predictable trends by adjusting its design to be efficient for the early detection of such trends. The adjustment involves changing the amount of memory the chart retains to detect persistent changes in location earlier.

In the zero-state case, Moustakides [6] proved that a step change of δ is best detected by using Page's [7] conventional CUSUM with the reference value k = δ/2. Gan [3] demonstrated that the conventional CUSUM with k = 0.5 is optimal in the zero-state in their Table 1 for a shift of one and standard normal distributed data. The adaptive CUSUM has been shown to be better at times at detecting small shifts in location than the conventional CUSUM with the optimal k value for that shift. For example, in the standard normal distribution case, the shift of 1 for the adaptive CUSUM is detected with an average run length (ARL); in Table 3 of Sparks [12] is 9.29 or 9.34, while the zero state optimal conventional CUSUM with k = 0.5 has an ARL of 9.34 (see also [5] Table 2). Hence, the adaptive CUSUM can have smaller out-of-control ARLs than the best CUSUM in the zero-state situation. The reason for this is that, for smaller shifts, the adaptive CUSUM can exploit the steady-state situation by making use of the local knowledge about the size of its shift. For unknown large shifts this is more difficult because one often flags the change before it can be accurately predicted. In other words the adaptive CUSUM

© 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, © 2018 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.

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

Table 1.   This, however, becomes more difficult for larger shifts. It only works for the smaller shifts where the steady state is reached while we are trying to accumulate enough memory to detect the change. For large shifts there is generally insufficient information on these shifts after its

1.75 3.986 3.945 3.931 3.932 3.916 3.911 3.913 3.910 3.928

Automation and sensor devices that measure very frequently means that data stream in these days in real-time, and therefore steady-state situations have now become more common than

occurrence to exploit it before it is detected.

δ

δ

δ

δ

1.00 9.379 9.309 9.272 9.263 9.289 9.329

1.20 7.093 7.045 7.017 7.020 7.000 7.039

1.40 5.640 5.577 5.533 5.509 5.519 5.538

1.60 4.512 4.499 4.504 4.498 4.499 4.509

1.65 4.316 4.284 4.287 4.280 4.294 4.274 4.302

1.70 4.159 4.114 4.097 4.099 4.099 4.096 4.083 4.098

1.45 5.375 5.308 5.254 5.233 5.223 5.228 5.252

1.50 5.143 5.076 4.983 4.979 4.980 4.969 4.981 4.992

1.25 6.676 6.642 6.609 6.567 6.578 6.575 6.602

1.30 6.334 6.295 6.260 6.196 6.194 6.195 6.203 6.220

1.05 8.757 8.670 8.622 8.628 8.595 8.635 8.632

1.10 8.206 8.112 8.050 8.028 8.025 8.019 8.029 8.053

1.15 7.742 7.631 7.551 7.514 7.499 7.478 7.477 7.503 7.513

k 0.45 0.475 0.5 0.525 0.55 0.6 0.625 0.65 0.675

1.35 6.013 5.971 5.942 5.869 5.857 5.848 5.854 5.849 5.865

k 0.5 0.5375 0.6 0.625 0.65 0.70 0.725 0.75 0.775

1.55 4.913 4.831 4.756 4.747 4.726 4.725 4.717 4.725 4.738

k 0.65 0.70 0.725 0.75 0.775 0.80 0.825 0.85 0.875

(h)

(g)

(f)

Adaptive CUSUM for Steady State Normal Data http://dx.doi.org/10.5772/intechopen.70752 139

Table 2. Optimal offset values (k) for detecting certain size shifts when the in-control ARL = 800.

Table 2.  This, however, becomes more difficult for larger shifts. It only works for the smaller shifts where the steady state is reached while we are trying to accumulate enough memory to detect the change. For large shifts there is generally insufficient information on these shifts after its occurrence to exploit it before it is detected.

Automation and sensor devices that measure very frequently means that data stream in these days in real-time, and therefore steady-state situations have now become more common than when the CUSUM was first advocated by Page [7]. Most applications in environmental sciences are steady state since the process cannot be stopped. The majority of service processes, although can be stopped, are hardly ever stopped and restarted. Thus, they may be referred to as steady-state processes.

CU

for the conventional CUSUM in the steady-state situation.

ACU

improve the early detection performance of the plan.

illustrate this are reported in Figure 1(a)–(c).

a near missed signal at time 71 the CU

the conventional CUSUM fails to signal.

observations sooner than the CUSUM with k = 0.25.

shift on the high side whenever

the adaptive CUSUM statistic:

at time = 81 the CU

t ð Þ¼ k max 0;CU

CU

t ð Þ¼ k max 0; ACU

Figure 1 plots the conventional CUSUM divided by its threshold (i.e., CU

t ð Þk =h kð Þ with k = 0.25 is almost identical to CU

where h(k) is the positive valued threshold that delivers a specified in-control ARL in the steady-state situation. Appendix A provides models for accurately predicting the thresholds

The adaptive CUSUM allows the reference value to change over time t and is given by using

and flags an out-breaks whenever this exceeds a threshold of approximately 1. The challenge in practice is how to change kt over time t to improve the early detection performance of the plan. An alternative approach that is explored in this paper is how to select (zt� kt)/h(kt) to

Sparks's [12] plan was based on the hypothesis that the zero-state optimal setting was going to be optimal in the steady-state situation. This is however, not the case. The examples that

and 0.2125 both designed to have an in-control ARL of 200) for 100 observations from a normal distribution. The first 80 observations are in-control standard normal data and the last 20 normally observations that are shifted on the high side by 0.5. Note that k = 0.25 is the value which is the zero-state optimal value established by Moustakides [6] for this shift, while k = 0.2125 is a better alternative in the steady-state situation. Note that prior to the change point

values with k = 0.25. This increase is enough to flag this change in the last 20 observations while

Figure 1(b) illustrates that fact that the CUSUM plan with k = 0.2125 is less likely to reset to zero than the CUSUM plan with k = 0.25 and therefore is likely to flag the change in the last 20

t�1 þ ð Þ zt � kt =h kð Þt

where k is referred to as the reference value that determines the level of past memory held by the CUSUM statistic. The resetting to zero of the CUSUM statistic is the process that controls the memory in the plan. Large values of k will make the CUSUM statistic operate like the memoryless Shewhart chart by frequently resetting to zero. Smaller values of k retain more historical information in the plan by resetting to zero less often. Therefore, practitioners would like to have large values of k when the shift is large and small values of k when shifts are small. Small values of k allow the CUSUM to accumulate more information thus having sufficient power to detect small shifts. The conventional CUSUM statistic signals an unusual location

t�1 þ zt � k (1)

Adaptive CUSUM for Steady State Normal Data http://dx.doi.org/10.5772/intechopen.70752 141

t ð Þk > h kð Þ (2)

(3)

t =h kð Þ for k = 0.25

t ð Þk =h kð Þ

t ð Þk =h kð Þ with k = 0.2125 but after

t ð Þk =h kð Þ with k = 0.2125 is higher than the CU

For this reason zero-state processes are less common, thus, revealing a scientific area that needs to be further researched.

## 2. Literature review

Sparks's [12] adaptive CUSUM improved the CUSUM early detection performance by appropriately adjusting the reference value k to improve its early detection performance. This paper will introduce and elaborate on a different approach to optimise equilibrium conditions and draw on observed outcomes. Jiang et al. [5] followed Sparks [12] in using the zero-state optimal reference value of the shift value divided by 2, but introduced a weighting function for the departures of the control variable from the zero-state optimal reference value. In particular, open-ended work should focus in optimising the CUSUM in steady-state situations (even for known shifts).

This paper starts by introducing the conventional CUSUM and the adaptive CUSUM statistics. It derives the thresholds for the CUSUM plans in steady-state situations for high-sided signals only. Low-sided charts can be established by symmetry and two-sided charts can be applied by simultaneously applying two one-sided charts and halving the in-control ARL of the high-sided chart. The high-sided charts for steady-state situations are designed to deliver a specific in-control ARL of either 100, 200, 300, …, 1000 (see Appendix A). Monitoring plans are defined in Sparks [14]. If the location is known in advance then this paper establishes the reference value closest to the best plan for the steady-state situation. A simulation study is carried out to find the CUSUM p best for the early detection of a known location shift.

Methods that compete with the adaptive CUSUM in terms of performance involve the simultaneous application of multiple CUSUMs with differing levels of memory [4, 12], combining Shewhart and CUSUM charts [8, 11], the adaptive EWMA [1] and multiple moving averages [13]. Ryu et al. [9] assumes the shift is known and optimises the CUSUM plan without mentioning whether it is based on zero or steady state, and therefore it must be viewed as competing methodology. However, this paper's contribution is on improving the out-of-control performance of the adaptive CUSUM plan in the steady-state situation and provides formulae to estimate the thresholds for the high-sided conventional CUSUM in steady-state situations.

## 3. CUSUM and adaptive CUSUM plans

Let yt the process variable measured at time t which has mean μ and variance σ2 . Define the standardised score as zt = (yt μ)/σ. Then Page's CUSUM plan for high-sided location changes is given by

$$\mathbb{C}\_{t}^{\mathrm{II}}(k) = \max\{0, \mathbb{C}\_{t-1}^{\mathrm{II}} + z\_t - k\} \tag{1}$$

where k is referred to as the reference value that determines the level of past memory held by the CUSUM statistic. The resetting to zero of the CUSUM statistic is the process that controls the memory in the plan. Large values of k will make the CUSUM statistic operate like the memoryless Shewhart chart by frequently resetting to zero. Smaller values of k retain more historical information in the plan by resetting to zero less often. Therefore, practitioners would like to have large values of k when the shift is large and small values of k when shifts are small. Small values of k allow the CUSUM to accumulate more information thus having sufficient power to detect small shifts. The conventional CUSUM statistic signals an unusual location shift on the high side whenever

when the CUSUM was first advocated by Page [7]. Most applications in environmental sciences are steady state since the process cannot be stopped. The majority of service processes, although can be stopped, are hardly ever stopped and restarted. Thus, they may be referred to

140 Quality Management Systems - a Selective Presentation of Case-studies Showcasing Its Evolution

For this reason zero-state processes are less common, thus, revealing a scientific area that

Sparks's [12] adaptive CUSUM improved the CUSUM early detection performance by appropriately adjusting the reference value k to improve its early detection performance. This paper will introduce and elaborate on a different approach to optimise equilibrium conditions and draw on observed outcomes. Jiang et al. [5] followed Sparks [12] in using the zero-state optimal reference value of the shift value divided by 2, but introduced a weighting function for the departures of the control variable from the zero-state optimal reference value. In particular, open-ended work should focus in optimising the CUSUM in steady-state situations

This paper starts by introducing the conventional CUSUM and the adaptive CUSUM statistics. It derives the thresholds for the CUSUM plans in steady-state situations for high-sided signals only. Low-sided charts can be established by symmetry and two-sided charts can be applied by simultaneously applying two one-sided charts and halving the in-control ARL of the high-sided chart. The high-sided charts for steady-state situations are designed to deliver a specific in-control ARL of either 100, 200, 300, …, 1000 (see Appendix A). Monitoring plans are defined in Sparks [14]. If the location is known in advance then this paper establishes the reference value closest to the best plan for the steady-state situation. A simulation study is

carried out to find the CUSUM p best for the early detection of a known location shift.

Let yt the process variable measured at time t which has mean μ and variance σ2

standardised score as zt = (yt μ)/σ. Then Page's CUSUM plan for high-sided location changes

. Define the

3. CUSUM and adaptive CUSUM plans

is given by

Methods that compete with the adaptive CUSUM in terms of performance involve the simultaneous application of multiple CUSUMs with differing levels of memory [4, 12], combining Shewhart and CUSUM charts [8, 11], the adaptive EWMA [1] and multiple moving averages [13]. Ryu et al. [9] assumes the shift is known and optimises the CUSUM plan without mentioning whether it is based on zero or steady state, and therefore it must be viewed as competing methodology. However, this paper's contribution is on improving the out-of-control performance of the adaptive CUSUM plan in the steady-state situation and provides formulae to estimate the thresholds for the high-sided conventional CUSUM in steady-state situations.

as steady-state processes.

2. Literature review

(even for known shifts).

needs to be further researched.

$$\mathsf{C}\_{t}^{\mathrm{cl}}(k) > h(k) \tag{2}$$

where h(k) is the positive valued threshold that delivers a specified in-control ARL in the steady-state situation. Appendix A provides models for accurately predicting the thresholds for the conventional CUSUM in the steady-state situation.

The adaptive CUSUM allows the reference value to change over time t and is given by using the adaptive CUSUM statistic:

$$A\mathcal{C}\_t^{\mathcal{U}}(k) = \max\left(0, A\mathcal{C}\_{t-1}^{\mathcal{U}} + (z\_t - k\_t)/h(k\_t)\right) \tag{3}$$

and flags an out-breaks whenever this exceeds a threshold of approximately 1. The challenge in practice is how to change kt over time t to improve the early detection performance of the plan. An alternative approach that is explored in this paper is how to select (zt� kt)/h(kt) to improve the early detection performance of the plan.

Sparks's [12] plan was based on the hypothesis that the zero-state optimal setting was going to be optimal in the steady-state situation. This is however, not the case. The examples that illustrate this are reported in Figure 1(a)–(c).

Figure 1 plots the conventional CUSUM divided by its threshold (i.e., CU t =h kð Þ for k = 0.25 and 0.2125 both designed to have an in-control ARL of 200) for 100 observations from a normal distribution. The first 80 observations are in-control standard normal data and the last 20 normally observations that are shifted on the high side by 0.5. Note that k = 0.25 is the value which is the zero-state optimal value established by Moustakides [6] for this shift, while k = 0.2125 is a better alternative in the steady-state situation. Note that prior to the change point at time = 81 the CU t ð Þk =h kð Þ with k = 0.25 is almost identical to CU t ð Þk =h kð Þ with k = 0.2125 but after a near missed signal at time 71 the CU t ð Þk =h kð Þ with k = 0.2125 is higher than the CU t ð Þk =h kð Þ values with k = 0.25. This increase is enough to flag this change in the last 20 observations while the conventional CUSUM fails to signal.

Figure 1(b) illustrates that fact that the CUSUM plan with k = 0.2125 is less likely to reset to zero than the CUSUM plan with k = 0.25 and therefore is likely to flag the change in the last 20 observations sooner than the CUSUM with k = 0.25.

Figure 1(c) exemplifies that the CUSUM plans with k = 0.2125 and k = 0.25 are almost identical for the first 60 in-control observations, but once the change occurs CUSUM with k = 0.2125 accelerates to the threshold quicker than the CUSUM plan with k = 0.25, and thus flagging this shift earlier. Extensive simulated examples not reported in this paper revealed that these plans, on most occasions, are almost identical. However, in a few examples as illustrated in Figure 1(a)–(c) the plan with k = 0.2125 exploits the situation better by being less likely to rest to zero and thus,

Adaptive CUSUM for Steady State Normal Data http://dx.doi.org/10.5772/intechopen.70752 143

This begs the question of what reference values k in the steady-state situations are better at detecting location changes from the in-control mean than k equal to shift divided by 2 that is

A simulation study was carried out that started with running through 25 in-control observations before generating the out-of-control situations. This was designed to simulate a steadystate situation prior to the change point. The thresholds for this process are given in Appendix A for the standard normal distribution. There is no loss of generality by assuming mean of zero and variance of one, however the results only apply to normally distributed data. The smallest out-of-control ARLs for various scenarios are presented in Table 1 for in-control ARL = 200,

The reference value with the smallest out-of-control ARL is highlighted in bold text, e.g., for incontrol ARL = 200 and a location shift of δ = 0.5 the near optimal steady state k is 0.2125 with an out-of-control ARL = 16.699 while the zero state optimal in the steady-state situation k = 0.25 delivers an out-of-control ARL = 16.847 (see Table 1(a)). In most cases the last entry in the rows of Tables 1 and 2 is the zero-state optimal value of k equal to the location change divided by 2. Notice that k = δ/2 is never the plan with the smallest out-of-control ARL—the k with the smallest out-of-control ARL is always smaller than δ/2; in other words the better plan which

The optimal reference value is reported in bold text in Table 2, for example, for in-control ARL = 800 and a location shift of δ = 0.5 the near optimal steady state k is 0.2375 with an out-ofcontrol ARL = 26.449 while the zero state optimal in the steady-state situation k = 0.25 delivers an out-of-control ARL = 26.543 (see Table 1(a)). Notice that relative to Table 1, k = δ/2 is closer to the plan with the smallest out-of-control ARL than in Table 1, that is, the k with the smallest out-ofcontrol ARL is always smaller than δ/2 but now the difference between the k with the smallest outof-control ARL and δ/2 is less than was found in Table 1. For this reason we expect less relative gain by optimising the adaptive CUSUM for the steady-state situation with larger in-control ARL.

5. Improving adaptive CUSUM performance for the steady-state situation

The EWMA statistic in Sparks [12] and Jiang et al. [5] is used to forecast the change δ. However, this forecast always under-estimates the change in location. This bias in prediction is more

more likely to flag an out-break in a steady-state situation earlier.

4. Near optimal steady-state plans when the shift is known

optimal for the zero-state.

and for in-control ARL = 800 in Table 2.

resets the CUSUM statistic to zero a little less often.

Figure 1. (a) Example 1 of when zero state optimal k = 0.25 does not do better than k = 0.2125. (b) Example 2 of when k = 0.2125 resets the CUSUM to zero than k = 0.25 and there has a better chance of detecting small shifts early. (c) Example 2 of when zero state optimal k = 0.25 does not do better than k = 0.2125.

Figure 1(c) exemplifies that the CUSUM plans with k = 0.2125 and k = 0.25 are almost identical for the first 60 in-control observations, but once the change occurs CUSUM with k = 0.2125 accelerates to the threshold quicker than the CUSUM plan with k = 0.25, and thus flagging this shift earlier. Extensive simulated examples not reported in this paper revealed that these plans, on most occasions, are almost identical. However, in a few examples as illustrated in Figure 1(a)–(c) the plan with k = 0.2125 exploits the situation better by being less likely to rest to zero and thus, more likely to flag an out-break in a steady-state situation earlier.

This begs the question of what reference values k in the steady-state situations are better at detecting location changes from the in-control mean than k equal to shift divided by 2 that is optimal for the zero-state.

## 4. Near optimal steady-state plans when the shift is known

A simulation study was carried out that started with running through 25 in-control observations before generating the out-of-control situations. This was designed to simulate a steadystate situation prior to the change point. The thresholds for this process are given in Appendix A for the standard normal distribution. There is no loss of generality by assuming mean of zero and variance of one, however the results only apply to normally distributed data. The smallest out-of-control ARLs for various scenarios are presented in Table 1 for in-control ARL = 200, and for in-control ARL = 800 in Table 2.

The reference value with the smallest out-of-control ARL is highlighted in bold text, e.g., for incontrol ARL = 200 and a location shift of δ = 0.5 the near optimal steady state k is 0.2125 with an out-of-control ARL = 16.699 while the zero state optimal in the steady-state situation k = 0.25 delivers an out-of-control ARL = 16.847 (see Table 1(a)). In most cases the last entry in the rows of Tables 1 and 2 is the zero-state optimal value of k equal to the location change divided by 2. Notice that k = δ/2 is never the plan with the smallest out-of-control ARL—the k with the smallest out-of-control ARL is always smaller than δ/2; in other words the better plan which resets the CUSUM statistic to zero a little less often.

The optimal reference value is reported in bold text in Table 2, for example, for in-control ARL = 800 and a location shift of δ = 0.5 the near optimal steady state k is 0.2375 with an out-ofcontrol ARL = 26.449 while the zero state optimal in the steady-state situation k = 0.25 delivers an out-of-control ARL = 26.543 (see Table 1(a)). Notice that relative to Table 1, k = δ/2 is closer to the plan with the smallest out-of-control ARL than in Table 1, that is, the k with the smallest out-ofcontrol ARL is always smaller than δ/2 but now the difference between the k with the smallest outof-control ARL and δ/2 is less than was found in Table 1. For this reason we expect less relative gain by optimising the adaptive CUSUM for the steady-state situation with larger in-control ARL.

## 5. Improving adaptive CUSUM performance for the steady-state situation

Figure 1. (a) Example 1 of when zero state optimal k = 0.25 does not do better than k = 0.2125. (b) Example 2 of when k = 0.2125 resets the CUSUM to zero than k = 0.25 and there has a better chance of detecting small shifts early. (c) Example

2 of when zero state optimal k = 0.25 does not do better than k = 0.2125.

142 Quality Management Systems - a Selective Presentation of Case-studies Showcasing Its Evolution

The EWMA statistic in Sparks [12] and Jiang et al. [5] is used to forecast the change δ. However, this forecast always under-estimates the change in location. This bias in prediction is more severe for large shifts where only a few observations can be used to optimise the CUSUM before the change is signalled. For this reason the EWMA statistic is thresholded to not fall below a certain minimum values, e.g.,

$$SP\_t = \max\left(\delta\_{min}, \alpha y\_t + (1 - \alpha) SP\_{t-1}\right) \tag{4}$$

Table 5. Comparison of adaptive CUSUM plans for in-control ARL = 300.

Table 4. Comparison of adaptive CUSUM plans for in-control ARL = 200.

k = SPt/2 k = SPt 1/2

k = SPt/2 k = SPt 1/2

Delta α = 0.2 α = 0.2 α = 0.6 α = 0.7

Delta α = 0.2 α = 0.2 α = 0.6 α = 0.7

0.00 199.979 200.897 200.328 200.006 0.50 17.009 18.291 15.380 15.641 0.75 9.996 9.971 9.122 9.255 1.00 6.944 6.662 6.453 6.488 1.25 5.240 4.948 4.996 4.948 1.50 4.179 3.949 3.990 3.984 1.75 3.472 3.303 3.367 3.325 2.00 2.968 2.864 2.928 2.855 2.25 2.594 2.541 2.580 2.510 2.50 2.306 2.303 2.317 2.231 2.75 2.085 2.126 2.116 2.024 3.00 1.904 1.984 1.952 1.852

hadj = 1.2877 hadj = 0.9215 hopt = 1.132637 hopt = 1.312637

Adaptive CUSUM for Steady State Normal Data http://dx.doi.org/10.5772/intechopen.70752 145

0.00 300.089 300.581 300.682 300.858 0.50 19.689 21.272 19.662 19.931 0.75 11.453 11.324 11.549 11.758 1.00 7.851 7.414 8.064 8.162 1.25 5.904 5.473 6.119 6.170 1.50 4.698 4.341 4.922 4.921 1.75 3.861 3.615 4.103 4.059 2.00 3.290 3.101 3.518 3.448 2.25 2.876 2.757 3.090 2.991 2.50 2.543 2.491 2.749 2.653 2.75 2.286 2.282 2.488 2.380 3.00 2.084 2.123 2.281 2.168

hadj = 1.2877 hadj = 0.9215 hopt = 1.168285 hopt = 1.351279

where 0 < α < 1, δmin is the smallest positive location change one wishes to detect early and SP0 = δmin. This paper takes δmin = 0.5 and α = 0.2. Since this forecast is biased and the change in location is unknown in advance it is difficult to know what value to use for the reference value kt given the knowledge of SPt. Sparks [12] used kt = SPt� 1/2 based on the assumption that this was the optimal zero-state situation. For additional information of adaptive plans see [10, 16, 18].

Given SPt under predicts the change and the optimal kt for in steady-state situation is generally lower than SPt � 1/2 (the EWMA one time ahead forecast divided by 2) or SPt/2 (the local smoothed value) this may be a good compromise strategy. When a change occurs then generally k = SPt/2 is less biased for this change than k = SPt � 1/2 .

In other words the local smoothed value SPt is used to establish k rather than the step-ahead forecast SPt � 1. This section explores whether this is a better alternative than the forecast. The comparisons of columns 2 and 3 in Tables 3–8 indicate that using the reference value equal to SPt/2 becomes less attractive as in-control ARL increases, for example, for in-control ARL equal to 100 it has the smaller out-of-control ARL in most cases, but when the in-control ARL = 800 it

Table 3. Comparison of adaptive CUSUM plans for in-control ARL = 100.

Table 4. Comparison of adaptive CUSUM plans for in-control ARL = 200.

severe for large shifts where only a few observations can be used to optimise the CUSUM before the change is signalled. For this reason the EWMA statistic is thresholded to not fall

144 Quality Management Systems - a Selective Presentation of Case-studies Showcasing Its Evolution

SPt ¼ max δmin; αyt þ ð Þ 1 � α SPt�1

where 0 < α < 1, δmin is the smallest positive location change one wishes to detect early and SP0 = δmin. This paper takes δmin = 0.5 and α = 0.2. Since this forecast is biased and the change in location is unknown in advance it is difficult to know what value to use for the reference value kt given the knowledge of SPt. Sparks [12] used kt = SPt� 1/2 based on the assumption that this was the optimal zero-state situation. For additional information of adaptive plans see [10, 16, 18].

Given SPt under predicts the change and the optimal kt for in steady-state situation is generally lower than SPt � 1/2 (the EWMA one time ahead forecast divided by 2) or SPt/2 (the local smoothed value) this may be a good compromise strategy. When a change occurs then gener-

In other words the local smoothed value SPt is used to establish k rather than the step-ahead forecast SPt � 1. This section explores whether this is a better alternative than the forecast. The comparisons of columns 2 and 3 in Tables 3–8 indicate that using the reference value equal to SPt/2 becomes less attractive as in-control ARL increases, for example, for in-control ARL equal to 100 it has the smaller out-of-control ARL in most cases, but when the in-control ARL = 800 it

Delta α = 0.2 α = 0.2 α = 0.6 α = 0.7

0.00 100.03 100.09 100.00 100.00 0.50 12.70 13.59 12.56 12.59 0.75 7.72 7.82 7.71 7.72 1.00 5.42 5.41 5.50 5.50 1.25 4.14 4.08 4.30 4.24 1.50 3.35 3.31 3.52 3.45 1.75 2.82 2.79 2.99 2.90 2.00 2.43 2.44 2.62 2.51 2.25 2.15 2.19 2.32 2.19 2.50 1.93 2.00 2.10 1.99 2.75 1.75 1.86 1.92 1.80 3.00 1.61 1.75 1.77 1.65

hadj = 1.2271 hadj = 0.9215 hopt = 1.005 hopt = 1.172

(4)

below a certain minimum values, e.g.,

ally k = SPt/2 is less biased for this change than k = SPt � 1/2 .

Table 3. Comparison of adaptive CUSUM plans for in-control ARL = 100.

k = SPt/2 k = SPt � 1/2

Table 5. Comparison of adaptive CUSUM plans for in-control ARL = 300.

Table 6. Comparison of adaptive CUSUM plans for in-control ARL = 400.

Table 7. Comparison of adaptive CUSUM plans for in-control ARL = 600.

is only preferred when delta = 0.5. As such, selecting k = SPt/2 is preferred if the in-control ARL = 100. However, its preference soon drops off as the in-control ARL increases from 200.

Now the Signal-to-Noise Ratio, SNR, (zt� kt)/h(kt) will be selected that will improve the detec-

for positive k values. The k is restricted to be greater than 0.22 in this paper which means we are less interested in location shifts less than 0.5 standard deviations. Note that SNRt < 0

Next, kt is chosen such that the Signal-to-Noise Ratio (zt � kt)/h(kt) is a maximum, denote

SNRt ¼ maxk

whenever zt < 0.22. The new adaptive CUSUM statistic is now defined by

t�1 þ ð Þ zt � kt =h kð Þt

zt � k

(5)

Et ¼ αzt þ ð Þ 1 � α Et�1 (6)

h kð Þ (7)

5.1. Attempts to improve on the adaptive plan of Sparks [12] in steady-state situations

t ð Þ¼ k max 0; ACU

tion performance of the plan. The EWMA smoothed trend in the zt is given by

Recall the adaptive CUSUM

ACU

Table 8. Comparison of adaptive CUSUM plans for in-control ARL = 800.

k = SPt/2 k = SPt � 1/2

Delta α = 0.2 α = 0.2 α = 0.6 α = 0.7

0.00 799.979 800.213 800.279 800.312 0.50 27.772 29.368 27.129 27.928 0.75 16.047 14.722 15.608 16.195 1.00 10.956 9.404 10.694 11.093 1.25 8.158 6.823 7.998 8.265 1.50 6.395 5.343 6.332 6.493 1.75 5.216 4.139 5.212 5.289 2.00 4.387 3.759 4.435 4.455 2.25 3.783 3.305 3.840 3.821 2.50 3.316 2.963 3.391 3.325 2.75 2.961 2.708 3.043 2.981 3.00 2.675 2.501 2.767 2.693

hadj = 1.4311 hadj = 0.909 hopt = 1.3042 hopt = 1.5196

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Table 8. Comparison of adaptive CUSUM plans for in-control ARL = 800.

Table 6. Comparison of adaptive CUSUM plans for in-control ARL = 400.

146 Quality Management Systems - a Selective Presentation of Case-studies Showcasing Its Evolution

k = SPt/2 k = SPt 1/2

Table 7. Comparison of adaptive CUSUM plans for in-control ARL = 600.

k = SPt/2 k = SPt 1/2

Delta α = 0.2 α = 0.2 α = 0.6 α = 0.7

0.00 398.492 399.897 400.127 400.369 0.50 21.831 23.357 21.662 22.120 0.75 12.875 12.201 12.670 12.999 1.00 8.896 7.991 8.776 8.992 1.25 6.663 5.902 6.644 6.745 1.50 5.269 4.648 5.306 5.345 1.75 4.333 3.872 4.413 4.401 2.00 3.674 3.326 3.776 3.726 2.25 3.187 2.941 3.302 3.233 2.50 2.815 2.649 2.938 2.845 2.75 2.512 2.421 2.648 2.558 3.00 2.288 2.249 2.416 2.316

Delta α = 0.2 α = 0.2 α = 0.6 α = 0.7

0.00 599.579 599.797 600.319 600.402 0.50 25.226 26.808 24.801 25.365 0.75 14.740 13.650 14.375 14.879 1.00 10.039 8.825 9.876 10.193 1.25 7.500 6.430 7.421 7.603 1.50 5.900 5.045 5.919 6.008 1.75 4.837 4.168 4.888 4.926 2.00 4.077 3.149 4.162 4.142 2.25 3.526 3.187 3.622 3.577 2.50 3.107 2.833 3.205 3.143 2.75 2.778 2.590 2.881 2.801 3.00 2.513 2.392 2.621 2.538

hadj = 1.4311 hadj = 0.907 hopt = 1.266595 hopt = 1.47165

hadj = 1.386 hadj = 0.9215 hopt = 1.267766 hopt = 1.484168

is only preferred when delta = 0.5. As such, selecting k = SPt/2 is preferred if the in-control ARL = 100. However, its preference soon drops off as the in-control ARL increases from 200.

#### 5.1. Attempts to improve on the adaptive plan of Sparks [12] in steady-state situations

Recall the adaptive CUSUM

$$A\mathcal{C}\_t^{\mathcal{U}}(k) = \max\left(0, A\mathcal{C}\_{t-1}^{\mathcal{U}} + (z\_t - k\_t)/h(k\_t)\right) \tag{5}$$

Now the Signal-to-Noise Ratio, SNR, (zt� kt)/h(kt) will be selected that will improve the detection performance of the plan. The EWMA smoothed trend in the zt is given by

$$E\_t = \alpha z\_t + (1 - \alpha)E\_{t-1} \tag{6}$$

Next, kt is chosen such that the Signal-to-Noise Ratio (zt � kt)/h(kt) is a maximum, denote

$$\text{SNR}\_t = \max\_k \left( \frac{z\_t - k}{h(k)} \right) \tag{7}$$

for positive k values. The k is restricted to be greater than 0.22 in this paper which means we are less interested in location shifts less than 0.5 standard deviations. Note that SNRt < 0 whenever zt < 0.22. The new adaptive CUSUM statistic is now defined by

$$N\mathbb{C}\_t^{\mathrm{I}}(k) = \max\{0, N\mathbb{C}\_{t-1}^{\mathrm{II}} + \mathrm{SNR}\_t\} \tag{8}$$

The threshold for this CUSUM is expected to be larger than 1. Therefore an increase in location is flagged when

$$N\mathbb{C}\_t^{\mathrm{II}}(k) > h\_{\mathrm{opt}} \tag{9}$$

Figure 2a adaptive CUSUM values as advocated in this paper for in-control ARL = 200 is

Figure 2b is the adaptive CUSUM of Sparks [12]. Both signal an increase in nitrogen dioxides

starting the CUSUM again at zero. The traditional adaptive CUSUM of Sparks [12] failed to

t ð Þk signals again on the 18 May 2016 after

Adaptive CUSUM for Steady State Normal Data http://dx.doi.org/10.5772/intechopen.70752 149

t ð Þk advocated in this paper for in-control ARL = 200. (b) The adaptive CUSUM of

plotted against the date for the period.

Figure 2. (a) The adaptive CUSUM NCU

Sparks [12].

signal a second time (Figure 2b).

on 8 May 2016, but the adaptive CUSUM values NCU

where hopt is selected to deliver a specified in-control ARL. The results in Tables 3–8 outline the performance of this plan relative to the traditional adaptive CUSUM plan of Sparks [12] in the case where the in-control ARL = 100, 200, 300, 400, 600 and 800 (in the 3rd column).

Table 3 indicates that the user should select the EWMA weights to be 0.7 to improve on the traditional adaptive CUSUM plan when 0 < δ ≤ 0.75 and δ ≥ 2.25 for in-control ARL = 200, but for all in-control ARL tried (in-control ARL6¼200) there is no advantage in using this plan in all cases except when δ = 0.5.

## 6. Example of application

The example of application is the nitrogen dioxide (NO2) values at Liverpool (a suburb in the western part of Sydney, Australia). Nitrogen dioxide primary gets into the air from the burning of fuel. High exposure to this can cause respiratory problems such as asthma (see WHO [17]). Nitrogen dioxide reacts with other chemicals in the air to form both particulate matter and ozone (see [2]). Both of these are harmful to humans and possibly animals when inhaled.

The data was downloaded from New South Wales (Australia) Heritage Foundation website on air pollution. Data ranged from the beginning of 2010 to the end of March 2017 and were daily averages.

The data up to the end of August 2016 were used as training data to fit both the (in-control) mean and standard deviation of the normal distribution using gamlss library in R [15]. The model had explanatory variables as time in days, day-of-the-week and harmonics. Harmonics are included because there were strong seasonal influences on nitrogen dioxide values at Liverpool. The qq-normal plot of standardised residuals of this model indicated that the normal assumption for the residuals was appropriate. This fitted model was then used to predict the mean and standard deviation for the period on 1 September 2016–31 March 2017 (taken as the expected value and standard deviation for in-control data).

The actual daily average nitrogen dioxide measures were standardised by subtracting their fitted mean and dividing by the fitted standard deviation. The adaptive CUSUM was then applied to these standardised scores to see if these values had increased significantly from expect during the period 1 September 2016–31 March 2017. The plan was designed to deliver an in-control ARL of 200. Whenever the chart flagged a significant increase the adaptive CUSUM was set equal to zero to see if the nitrogen dioxide levels remained significantly higher than expected.

NCU

148 Quality Management Systems - a Selective Presentation of Case-studies Showcasing Its Evolution

is flagged when

cases except when δ = 0.5.

inhaled.

averages.

higher than expected.

6. Example of application

t ð Þ¼ k max 0; NCU

NCU

case where the in-control ARL = 100, 200, 300, 400, 600 and 800 (in the 3rd column).

The threshold for this CUSUM is expected to be larger than 1. Therefore an increase in location

where hopt is selected to deliver a specified in-control ARL. The results in Tables 3–8 outline the performance of this plan relative to the traditional adaptive CUSUM plan of Sparks [12] in the

Table 3 indicates that the user should select the EWMA weights to be 0.7 to improve on the traditional adaptive CUSUM plan when 0 < δ ≤ 0.75 and δ ≥ 2.25 for in-control ARL = 200, but for all in-control ARL tried (in-control ARL6¼200) there is no advantage in using this plan in all

The example of application is the nitrogen dioxide (NO2) values at Liverpool (a suburb in the western part of Sydney, Australia). Nitrogen dioxide primary gets into the air from the burning of fuel. High exposure to this can cause respiratory problems such as asthma (see WHO [17]). Nitrogen dioxide reacts with other chemicals in the air to form both particulate matter and ozone (see [2]). Both of these are harmful to humans and possibly animals when

The data was downloaded from New South Wales (Australia) Heritage Foundation website on air pollution. Data ranged from the beginning of 2010 to the end of March 2017 and were daily

The data up to the end of August 2016 were used as training data to fit both the (in-control) mean and standard deviation of the normal distribution using gamlss library in R [15]. The model had explanatory variables as time in days, day-of-the-week and harmonics. Harmonics are included because there were strong seasonal influences on nitrogen dioxide values at Liverpool. The qq-normal plot of standardised residuals of this model indicated that the normal assumption for the residuals was appropriate. This fitted model was then used to predict the mean and standard deviation for the period on 1 September 2016–31 March 2017

The actual daily average nitrogen dioxide measures were standardised by subtracting their fitted mean and dividing by the fitted standard deviation. The adaptive CUSUM was then applied to these standardised scores to see if these values had increased significantly from expect during the period 1 September 2016–31 March 2017. The plan was designed to deliver an in-control ARL of 200. Whenever the chart flagged a significant increase the adaptive CUSUM was set equal to zero to see if the nitrogen dioxide levels remained significantly

(taken as the expected value and standard deviation for in-control data).

t�1 þ SNRt

(8)

t ð Þk > hopt (9)

Figure 2. (a) The adaptive CUSUM NCU t ð Þk advocated in this paper for in-control ARL = 200. (b) The adaptive CUSUM of Sparks [12].

Figure 2a adaptive CUSUM values as advocated in this paper for in-control ARL = 200 is plotted against the date for the period.

Figure 2b is the adaptive CUSUM of Sparks [12]. Both signal an increase in nitrogen dioxides on 8 May 2016, but the adaptive CUSUM values NCU t ð Þk signals again on the 18 May 2016 after starting the CUSUM again at zero. The traditional adaptive CUSUM of Sparks [12] failed to signal a second time (Figure 2b).

## 7. Conclusions and further work

Although the new adaptive CUSUM has promise, the SNRt proved too volatile to be efficient. There may be merit in establishing a smoother version of SNRt that is less noisy. If future location shifts are known, then this paper offers the mean of selecting an optimal adaptive CUSUM plan.

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## A. Appendix

## Author details

Ross Sparks

Address all correspondence to<EMAIL_ADDRESS>
Data61, CSIRO, Sydney, Australia

#### References

7. Conclusions and further work

Fitted model for h(k)

100 h(k) = 0.3794337 2.9630562 log(k) + 1.9600587k 0.8024828k

200 h(k) = 2.828476 4.867645 log(k) + 4.704948k 1.827205k log(k) 300 h(k) = 3.574586 5.639812 log(k) + 5.650032k 2.177893k log(k) 400 h(k) = 4.39191859 6.32066081 log(k) + 6.67882498k 0.06873969k

500 h(k) = 5.44288223 7.02105471 log(k) + 7.68319645k + 0.08688656k

600 h(k) = 6.602602 7.687670 log(k) + 8.825719k + 0.196071k

700 h(k) = 8.0773942 8.4028196 log(k) + 9.9107572k + 0.6595734k

800 h(k) = 8.9383214 8.9021000 log(k) + 10.7584243k + 0.7361421k

900 h(k) = 9.0757848 9.1040296 log(k) + 10.9300859k + 0.7607276k

1000 h(k) = 8.84991553 9.31320632 log(k) + 11.10662579k + 0.40968650k

(k < 0.675) (0.11040543 + 0.09135357 k + 0.11203402 k

CUSUM plan.

A. Appendix

In-control ARL

Author details

Address all correspondence to<EMAIL_ADDRESS>
chart. Technometrics. 2003;45(3):199-207

Data61, CSIRO, Sydney, Australia

Ross Sparks

References

Although the new adaptive CUSUM has promise, the SNRt proved too volatile to be efficient. There may be merit in establishing a smoother version of SNRt that is less noisy. If future location shifts are known, then this paper offers the mean of selecting an optimal adaptive

150 Quality Management Systems - a Selective Presentation of Case-studies Showcasing Its Evolution

2 + 0.9033659 log(k)k

2 3.996312k log(k)

2 ) 2 5.3895806k log(k)

2 5.9389200k log(k)

2 6.0276468 k log(k)

2 5.33730283k log(k) + as . factor

2 2.50144146k log(k)

2 3.22718165k log(k)

[1] Capizzi G, Masarotto G. An adaptive exponentially weighted moving average control

[2] Gamon LF, White JM, Wille U. Oxidative damage of aromatic dipeptides by the environmental oxidants NO2 and O3. Organic & Biomolecular Chemistry. 2014;12(41):8280-8287

**Chapter 8**

Provisional chapter

**Control Charts to Enhance Quality**

Control Charts to Enhance Quality

Additional information is available at the end of the chapter

Control charts are important tools of statistical quality control to enhance quality. Quality improvement methods have been applied in the last few 10 years to fulfill the needs of consumers. The product has to retain the desired properties with the least possible defects, while maximizing profit. There are natural variations in production, but there are also assignable causes which do not form part of chance. Control charts are used to monitor production; in particular, their application may serve as an "early warning" index regarding potential "out-of-control" processes. In order to keep production under control, different control charts which are prepared for dissimilar cases are established incorporating upper and lower control limits. There are a number of control charts in use and are grouped mainly as control charts for variables and control charts for attributes. Points plotted on the charts may reveal certain patterns, which in turn allows the user to obtain specific information. Patterns showing deviations from normal behavior are raw material, machine setting or measuring method, human, and environmental factors, inadvertently affecting the quality of product. The information obtained from control charts assists the user to take corrective actions, hence opting for specified nominal values enhancing as

DOI: 10.5772/intechopen.73237

Keywords: quality, quality improvement, control charts, upper and lower control limits,

Quality is regarded as an important build-in feature of a product, whose function is to fit ones needs, while showing no defects. In addition to this, the price has to be right, so that the product

> © 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 eproduction in any medium, provided the original work is properly cited.

> © 2018 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.

individual, variable, attribute, interpretation, corrective action

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.73237

Nefise Gönül Şengöz

Nefise Gönül Şengöz

Abstract

such quality.

1. Introduction

## **Chapter 8**

Provisional chapter

## **Control Charts to Enhance Quality** Control Charts to Enhance Quality

Nefise Gönül Şengöz Nefise Gönül Şengöz

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.73237

#### Abstract

Control charts are important tools of statistical quality control to enhance quality. Quality improvement methods have been applied in the last few 10 years to fulfill the needs of consumers. The product has to retain the desired properties with the least possible defects, while maximizing profit. There are natural variations in production, but there are also assignable causes which do not form part of chance. Control charts are used to monitor production; in particular, their application may serve as an "early warning" index regarding potential "out-of-control" processes. In order to keep production under control, different control charts which are prepared for dissimilar cases are established incorporating upper and lower control limits. There are a number of control charts in use and are grouped mainly as control charts for variables and control charts for attributes. Points plotted on the charts may reveal certain patterns, which in turn allows the user to obtain specific information. Patterns showing deviations from normal behavior are raw material, machine setting or measuring method, human, and environmental factors, inadvertently affecting the quality of product. The information obtained from control charts assists the user to take corrective actions, hence opting for specified nominal values enhancing as such quality.

DOI: 10.5772/intechopen.73237

Keywords: quality, quality improvement, control charts, upper and lower control limits, individual, variable, attribute, interpretation, corrective action

## 1. Introduction

Quality is regarded as an important build-in feature of a product, whose function is to fit ones needs, while showing no defects. In addition to this, the price has to be right, so that the product

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons © 2018 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.

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.

may serve its designed life span. Another aspect of quality is that the product has to show the user a favorable characteristic while used other than the aim of the user to buy the product. When all the mentioned measures are met within the product, it may be regarded as a quality product.

provide visual support about the deviations in the characteristics [2]. In doing so, they prevent

Control Charts to Enhance Quality

155

http://dx.doi.org/10.5772/intechopen.73237

Quality improvement tools are mainly process flow diagrams, cause-and-effect (fishbone) diagrams, check sheets, histograms, scatter plots, Pareto diagrams, and control charts. The aim of this chapter is to focus on the use of only the control charts and provide a qualitative and quantitative insight. As such, it will present industrial cases regarding their use and type. In addition to this, it will discuss on how they are designed, prepared, and interpreted together

• Control charts for variables, that is, individual measurements control charts, means control charts, ranges control charts, and standard deviation control charts with industrial

• Control charts for attributes, that is, control charts for fraction nonconforming, control charts for the number of nonconforming items, control charts for conformities per unit,

Control charts provide higher efficiency in production, decrease defects and faulty production, increase profit, and diminish costs. These are some of the reasons why control charts are widely used in industry. Indeed, their area of application is quite wide and covers nearly everything from service organizations and providers to financial consulting offices, as well as

It is worth mentioning at this point that in nature as well as in service and production companies, no two products of the same substance are exactly the same. This implies that at

and control charts for nonconformities with industrial applications;

the formation of defects and increase and develop the efficiency of the processes.

1.1. Aims and objectives

with research concerning control charts.

• General guidelines to prepare control charts;

• Presentation of control charts in the area of quality control;

In doing so, this work will include:

• Special cases for control charts; • Interpretation of control charts;

in various other applications in daily life.

• Research on control charts.

2. Literature review

• Design of a control chart; • Types of control charts;

applications;

Some types of production are done by one person, let us say a tailor; this person is responsible of every step of the product either machine performed, or by hand. As such, that person would take care of any defects as soon as these occur. In addition to this, that one person would add or deduct so-called "excitement" features in the product according to the consumer's taste. This kind of production is called the mentor-protege type. Henry Ford introduced and implemented mass production, where every step of the production is done by someone else with a different machine. Since many people and machines are involved in the production, the chance of deviations and defects increases and may cause quality-specific problems. Furthermore, since the operators do not know who the consumer they are producing for in mass production, research and development departments were created to fulfill the "excitement" features, since this work had to be done by other people than the operator; additionally, research and development departments serve to aim produced goods to different markets.

In order to effectively manage and eliminate quality-specific problems, a number of quality control methods were developed. The following encapsulates some of these:

Statistical quality control is used widely in the modern business world. Indeed, control charts are deemed as one of the primary techniques to enhance quality. Gathering data to prepare a control chart is done according to many national and international standards like British Standards (BS), American Standards (ASTM), German Standards (DIN), Turkish Standards (TSE), etc. Variations in due time or sample order are examined by control charts in order to keep production under control according to the product's desired properties. The purpose of this chapter is to highlight the arising benefits of using control charts and elaborate their impetus on industrial case studies such as to keep production under control, to eliminate defects, and to increase profit, if not, a full understanding of what is going on in production or service will not be conceived.

A process is a system of bonds worked altogether to produce a specific outcome or factors which affect the production and the quality of a product or a function. In order a process to achieve the intended result, the causes of the mentioned process have to be kept under control. To this end, control charts are used [1]. The latter is prepared with numerical data of a particular characteristic of the product, which is controlled. Additionally, control charts provide visual support about the deviations in the characteristics [2]. In doing so, they prevent the formation of defects and increase and develop the efficiency of the processes.

#### 1.1. Aims and objectives

may serve its designed life span. Another aspect of quality is that the product has to show the user a favorable characteristic while used other than the aim of the user to buy the product. When all the mentioned measures are met within the product, it may be regarded as a quality product.

154 Quality Management Systems - a Selective Presentation of Case-studies Showcasing Its Evolution

Some types of production are done by one person, let us say a tailor; this person is responsible of every step of the product either machine performed, or by hand. As such, that person would take care of any defects as soon as these occur. In addition to this, that one person would add or deduct so-called "excitement" features in the product according to the consumer's taste. This kind of production is called the mentor-protege type. Henry Ford introduced and implemented mass production, where every step of the production is done by someone else with a different machine. Since many people and machines are involved in the production, the chance of deviations and defects increases and may cause quality-specific problems. Furthermore, since the operators do not know who the consumer they are producing for in mass production, research and development departments were created to fulfill the "excitement" features, since this work had to be done by other people than the operator; additionally, research and development departments serve to aim produced goods to different markets.

In order to effectively manage and eliminate quality-specific problems, a number of quality

Statistical quality control is used widely in the modern business world. Indeed, control charts are deemed as one of the primary techniques to enhance quality. Gathering data to prepare a control chart is done according to many national and international standards like British Standards (BS), American Standards (ASTM), German Standards (DIN), Turkish Standards (TSE), etc. Variations in due time or sample order are examined by control charts in order to keep production under control according to the product's desired properties. The purpose of this chapter is to highlight the arising benefits of using control charts and elaborate their impetus on industrial case studies such as to keep production under control, to eliminate defects, and to increase profit, if not, a full

A process is a system of bonds worked altogether to produce a specific outcome or factors which affect the production and the quality of a product or a function. In order a process to achieve the intended result, the causes of the mentioned process have to be kept under control. To this end, control charts are used [1]. The latter is prepared with numerical data of a particular characteristic of the product, which is controlled. Additionally, control charts

understanding of what is going on in production or service will not be conceived.

control methods were developed. The following encapsulates some of these:

• Quality control,

• Total quality control,

• Quality management, • Quality improvement,

• Total quality management,

• Six-sigma quality management, etc.

Quality improvement tools are mainly process flow diagrams, cause-and-effect (fishbone) diagrams, check sheets, histograms, scatter plots, Pareto diagrams, and control charts. The aim of this chapter is to focus on the use of only the control charts and provide a qualitative and quantitative insight. As such, it will present industrial cases regarding their use and type. In addition to this, it will discuss on how they are designed, prepared, and interpreted together with research concerning control charts.

In doing so, this work will include:

Control charts provide higher efficiency in production, decrease defects and faulty production, increase profit, and diminish costs. These are some of the reasons why control charts are widely used in industry. Indeed, their area of application is quite wide and covers nearly everything from service organizations and providers to financial consulting offices, as well as in various other applications in daily life.

### 2. Literature review

It is worth mentioning at this point that in nature as well as in service and production companies, no two products of the same substance are exactly the same. This implies that at least two of the same substance or characteristic are always different, or at least there is a small difference between them. This, however, is normal as long as it affects small variations. To produce every piece in a lot exactly to the specified nominal characteristic is both hard and costly. The measurements of some quality characteristic like length, width, temperature, weight, etc., vary slightly and maybe unavoidable. This variability depends on equipment, machinery, materials, equipment, environment, people, etc., and is acceptable. These types of variability are referred to as "normal", "random", or "natural".

• Knowing how the production proceeds,

cesses even they do not exist;

• Increasing production by doing it right the first time so to prevent defects,

• Making it easier to find the factors that negatively affect the process;

• Used to seek if the desired efficiency of a machine is achieved; • Useful in decreasing the variations in a product or in a process;

• Useful in decreasing the number of rejected pieces or waste;

• Enabling the specifications and orders at a more realistic level;

• Used in deciding the renewal time of the production machines;

• Substantial reference in research and development practices;

• Ensuring to decrease the cost of testing and control;

• Expedient in keeping sensitive and reliable records;

• Helpful in making the processes more stable;

present to the managers;

• Used in stocks control [5].

2.1. Design of a control chart

• Helpful in cost and financial analysis;

chemicals, etc., in a certain period of time.

analyzing the patterns occurring on the control chart

• Being aware of the effects of raw material, machine, worker, and environmental factors by

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• Saving time by preventing the error of searching for special reasons that effect the pro-

• Advantageous in preparation of reports near to real about the processes or operations to

The areas where control charts can be used are areas such as production-not least on say, count of the yarn or the weight of fabric in textiles, costs, sales, circulation of workers, material,

Quality control charts are statistical technique tools which have a wide application in scientific research, in industry, and even in daily life. This concept makes the use of control charts as important as cost control and material control. Information about the design and types of control charts and general guidelines to prepare control charts, and the likes are given below.

A control chart is a graph mainly derived from a normal distribution curve. The y-axis denotes a quality characteristic or a particular characteristic of the product or process, which is controlled and is marked in units, in which the test value is expressed. The x-axis consists of time

• Diminishing costs,

In view of the above, it is preferred that the variability has to be reduced as much as possible in the process, if it is not eliminated. The distances of the points from the mean line give the user information about its variability. There are chance causes of variation in statistical control, but there are also assignable causes which are not a part of the chance causes. These show important, large, and unusual differences. The reasons for this may be:

The above may cater for the "abnormal" or "unnatural" variations. In a production where the aim is to achieve quality and to meet the consumers' requirements, the presence of assignable causes may draw the process out-of-control. Since the objective of studied quality characteristic is to be stable and repeatable, the occurrence of assignable causes must be detected instantly and the investigation of the process and corrective action ought to take place before further nonconforming units are manufactured. Control charts are widely used in order to interpret the variability a characteristic possesses between nominal and actual settings. The differences between "normal" and "abnormal" variations are detected, and the characteristic is kept under control by taking all the necessary measures. The purpose of control charts in quality control is prevention, which is better than cure [3].

The amount of variation to be allowed in any manufacturing process is of paramount importance. It is impossible to examine the records of past data and evaluate data by looking and thinking without doing statistical calculations.

In some factories, technical staff checks out the data and estimates on an ad hoc level the limits of the process. These may be too wide or too narrow, which in turn, may be both affecting the production negatively causing it to go out-of-control. If the limits are too wide, the process will posses an excess of variation; if it is too narrow, extra work may be required so as to maintain set limits. It is worth noting at this point, both of them prevent corrective action to take place which is suitable for production. On the other hand, when the limits are calculated on a scientific basis, the exact amount of expected variation in a product will be determined and will be confidently used, so guesswork will be eliminated [4]. Examples for limits can be seen in Figures 6–12.

Shewhart developed the control charts first in 1924 and are as such called Shewhart control charts. The usage of control charts became common as its benefits were recognized in due time. Its benefits can be listed as:

least two of the same substance or characteristic are always different, or at least there is a small difference between them. This, however, is normal as long as it affects small variations. To produce every piece in a lot exactly to the specified nominal characteristic is both hard and costly. The measurements of some quality characteristic like length, width, temperature, weight, etc., vary slightly and maybe unavoidable. This variability depends on equipment, machinery, materials, equipment, environment, people, etc., and is acceptable. These types of

In view of the above, it is preferred that the variability has to be reduced as much as possible in the process, if it is not eliminated. The distances of the points from the mean line give the user information about its variability. There are chance causes of variation in statistical control, but there are also assignable causes which are not a part of the chance causes. These show

The above may cater for the "abnormal" or "unnatural" variations. In a production where the aim is to achieve quality and to meet the consumers' requirements, the presence of assignable causes may draw the process out-of-control. Since the objective of studied quality characteristic is to be stable and repeatable, the occurrence of assignable causes must be detected instantly and the investigation of the process and corrective action ought to take place before further nonconforming units are manufactured. Control charts are widely used in order to interpret the variability a characteristic possesses between nominal and actual settings. The differences between "normal" and "abnormal" variations are detected, and the characteristic is kept under control by taking all the necessary measures. The purpose of control charts in quality control is

The amount of variation to be allowed in any manufacturing process is of paramount importance. It is impossible to examine the records of past data and evaluate data by looking and

In some factories, technical staff checks out the data and estimates on an ad hoc level the limits of the process. These may be too wide or too narrow, which in turn, may be both affecting the production negatively causing it to go out-of-control. If the limits are too wide, the process will posses an excess of variation; if it is too narrow, extra work may be required so as to maintain set limits. It is worth noting at this point, both of them prevent corrective action to take place which is suitable for production. On the other hand, when the limits are calculated on a scientific basis, the exact amount of expected variation in a product will be determined and will be confidently used, so guesswork will be eliminated [4]. Examples for limits can be seen

Shewhart developed the control charts first in 1924 and are as such called Shewhart control charts. The usage of control charts became common as its benefits were recognized in due

variability are referred to as "normal", "random", or "natural".

• Material is taken from a different lot,

prevention, which is better than cure [3].

in Figures 6–12.

time. Its benefits can be listed as:

thinking without doing statistical calculations.

• Any kind of "operator error".

• The machine setter makes a new setting,

important, large, and unusual differences. The reasons for this may be:

156 Quality Management Systems - a Selective Presentation of Case-studies Showcasing Its Evolution

The areas where control charts can be used are areas such as production-not least on say, count of the yarn or the weight of fabric in textiles, costs, sales, circulation of workers, material, chemicals, etc., in a certain period of time.

Quality control charts are statistical technique tools which have a wide application in scientific research, in industry, and even in daily life. This concept makes the use of control charts as important as cost control and material control. Information about the design and types of control charts and general guidelines to prepare control charts, and the likes are given below.

#### 2.1. Design of a control chart

A control chart is a graph mainly derived from a normal distribution curve. The y-axis denotes a quality characteristic or a particular characteristic of the product or process, which is controlled and is marked in units, in which the test value is expressed. The x-axis consists of time intervals or sample number. There is a center line, which is the average of the value of the studied matter or may also indicate the nominal value. The upper boundary characterizes the upper control limit (UCL), while the lower designates the lower control limit (LCL), respectively. The gathered data are plotted in sequence, and then, the pattern occurring on the chart is interpreted. A sample of a control chart is given in Figure 1.

The center line of a control chart stands from the past data or new data got from the measurements in the process or applied from what the consumer wants. If the clients have specified limits for their orders, production has to be done according to the specification limits of the client. In this case, the UCL and LCL have to be in the specification limits (Figure 4). If the control limits take place out of the specification limits (Figure 4), then that is an undesirable

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Figure 3. Warning and action limits for small samples.

Figure 4. Placement of UCL and LCL according to specification limits.

Figure 1. Sample of a control chart.

As can be seen from Figure 1, there is a close relationship between the normal distribution curve and the control chart. Control charts are constructed on the basis of expanding the sigma limits above and below of the mean. By taking a deeper look, it can be expressed that expansion of 1.962σ from the mean may be regarded as the "warning limit," and the expansion of 3.09σ from the mean is the "action limit" for large samples (Figure 2). Similarly, 2σ/√n and 3σ/√n are the same limits, respectively, for small samples (Figure 3) [6].

Figure 2. Warning and action limits for large samples.

Figure 3. Warning and action limits for small samples.

intervals or sample number. There is a center line, which is the average of the value of the studied matter or may also indicate the nominal value. The upper boundary characterizes the upper control limit (UCL), while the lower designates the lower control limit (LCL), respectively. The gathered data are plotted in sequence, and then, the pattern occurring on the chart

As can be seen from Figure 1, there is a close relationship between the normal distribution curve and the control chart. Control charts are constructed on the basis of expanding the sigma limits above and below of the mean. By taking a deeper look, it can be expressed that expansion of 1.962σ from the mean may be regarded as the "warning limit," and the expansion of 3.09σ from the mean is the "action limit" for large samples (Figure 2). Similarly, 2σ/√n and

3σ/√n are the same limits, respectively, for small samples (Figure 3) [6].

Figure 1. Sample of a control chart.

Figure 2. Warning and action limits for large samples.

is interpreted. A sample of a control chart is given in Figure 1.

158 Quality Management Systems - a Selective Presentation of Case-studies Showcasing Its Evolution

The center line of a control chart stands from the past data or new data got from the measurements in the process or applied from what the consumer wants. If the clients have specified limits for their orders, production has to be done according to the specification limits of the client. In this case, the UCL and LCL have to be in the specification limits (Figure 4). If the control limits take place out of the specification limits (Figure 4), then that is an undesirable

Figure 4. Placement of UCL and LCL according to specification limits.

condition because the product will be manufactured with a quality characteristic range that the client does not want, thus resulting in an inferior quality product.

Each type has different kinds of control charts particularly for the case studied. The most

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Others are s2 control chart, moving range control charts, and regression control chart. The main kinds of control charts for attributes are foremost p-, np-, u-, and c-control charts. Others

There are control charts for special uses in literature which can be listed as cumulative sum control charts, moving average control chart, x-bar and R-control charts for short production runs, attributes control charts for short production runs, modified and acceptance control charts, group control charts for multiple-stream processes, chi-square control chart, difference control charts, control charts for contrasts, run sum and zone control charts, adaptive control charts, moving average control charts, residual control charts, control charts for six-sigma processes, acceptance control charts, T2 control charts, Hotelling T2 control charts, Exponentially Weighted Moving Average (EWMA) control charts, exponentially weight means square control charts, multivariate EWMA control charts, one-sided EWMA control charts, moving

important kinds of control charts for variables are mainly

are standardized control charts, g control charts, and h control charts.

centerline EWMA control charts, and one-sided CUSUM control chart [7].

6. Continue to plot the new values collected in due time on the chart;

It is apparent from the last step, as the production proceeds, new values accumulate and these new values should be plotted on the same control chart with the UCL and LCL calculated from the first values of the same production. This procedure guarantees that the properties of the

In the first preparation of the control chart, if an assignable cause is found in the data collected, that point is discarded and the trial control limits are recalculated, using only the remaining

2.3. General guidelines to prepare control charts

1. Obtain a set of values;

3. Do the needed calculations;

4. Draw the control chart;

points.

Steps to prepare control charts in general are as follows:

2. Decide which kind of a control chart to prepare;

5. Plot the values in Step 1 on the control chart;

7. Interpret the pattern occurring on the chart.

first products and the rest lie in the same control limits.

• Individual measurements control chart (x),

• Standard deviation control chart (s).

• Means control chart (x), • Ranges control chart (R),

3σ expansion means 6σ expansion from the UCL and LCL in total. From a normal distribution diagram, it is known that the area under the diagram corresponds to a 99.73% of probability. This means that the points used in the preparation of control charts will be included in the study with a 99.73% probability (Figure 5).

Figure 5. Representation of 99.73% probability.

Control charts are quality technique tools that may trigger an alarm. If a value exceeds the warning limit above or below, production may continue, but the reason for this variation must be investigated and corrective action must be taken.

In obtaining data from a process, sampling is performed by using small sample sizes. Concerning small samples, sensitivity of the control chart is increased by statistical methods, and the warning limit and the action limit are combined to be expressed as UCL and LCL. So, if a value gets close to one of these limits, it is understood that it is not needed to stop production but search for the reason of this variation and to correct it. Likewise, if a value crosses one of these limits, action has to be taken and production must be stopped before searching. Sensitivity, sample size, and sampling frequency (specific and equal time intervals) are important factors regarding the performance of the control chart. Sampling frequency must be in accordance with the production processes.

#### 2.2. Types of control charts

Control charts have two main types according to the way the values used are obtained. Values can be obtained by measuring on a numerical scale, that is, counting, calculating, by using a testing instrument, or by deriving proportions of judgments. If they are conforming or nonconforming, one would look at their certain attributes they have to possess so as to express a case. If the values used are obtained by measuring, then they are called control charts for variables. If the values used are obtained by deriving proportions, then they are called control charts for attributes. These charts apply for different process-specific cases in processes, so that each can be evaluated on its own.

Each type has different kinds of control charts particularly for the case studied. The most important kinds of control charts for variables are mainly

condition because the product will be manufactured with a quality characteristic range that the

3σ expansion means 6σ expansion from the UCL and LCL in total. From a normal distribution diagram, it is known that the area under the diagram corresponds to a 99.73% of probability. This means that the points used in the preparation of control charts will be included in the

Control charts are quality technique tools that may trigger an alarm. If a value exceeds the warning limit above or below, production may continue, but the reason for this variation must

In obtaining data from a process, sampling is performed by using small sample sizes. Concerning small samples, sensitivity of the control chart is increased by statistical methods, and the warning limit and the action limit are combined to be expressed as UCL and LCL. So, if a value gets close to one of these limits, it is understood that it is not needed to stop production but search for the reason of this variation and to correct it. Likewise, if a value crosses one of these limits, action has to be taken and production must be stopped before searching. Sensitivity, sample size, and sampling frequency (specific and equal time intervals) are important factors regarding the performance of the control chart. Sampling frequency must

Control charts have two main types according to the way the values used are obtained. Values can be obtained by measuring on a numerical scale, that is, counting, calculating, by using a testing instrument, or by deriving proportions of judgments. If they are conforming or nonconforming, one would look at their certain attributes they have to possess so as to express a case. If the values used are obtained by measuring, then they are called control charts for variables. If the values used are obtained by deriving proportions, then they are called control charts for attributes. These charts apply for different process-specific cases in processes, so that

client does not want, thus resulting in an inferior quality product.

160 Quality Management Systems - a Selective Presentation of Case-studies Showcasing Its Evolution

study with a 99.73% probability (Figure 5).

be investigated and corrective action must be taken.

Figure 5. Representation of 99.73% probability.

be in accordance with the production processes.

2.2. Types of control charts

each can be evaluated on its own.