To remain competitive and to provide timely and accurate services, the decision maker or system analyst view the reliability and maintainability issues as a part of corporate quest to improve quality of the products/processes and services delivered. But the collected or available data available from the historical records are mostly uncertain, limited and imprecise in nature. Thus in such situation(s), it is difficult, if not impossible, to analyze the behavior and performance of the system up to desired degree of accuracy. Thus attempt has been made by the author for analyzing the behavior and performance of the system using Vague Lambda–Tau methodology. Intuitionistic fuzzy set theory has been used for representing the classical(crisp) data into triangular fuzzy numbers because intuitionistic sets are characterized by a truth membership function and false membership functions (non-membership functions) so that sum of both values is less than 1. Sensitivity analysis has also been performed and the effects on system mean time between failures are addressed. The performance analysis of the system has been investigated through a composite measure of reliability, availability and maintainability (RAM) called RAM-Index which explore the effect of failure/repair rates on system performance. Based on their performance, the most critical component of the system has been investigated. The methodology improves the shortcomings of the existing probabilistic approaches and gives a better understanding of the system behavior through its graphical representation. The pulping unit of a paper mill situated in a northern part of India, producing approximately 200ton of paper per day, has been considered to demonstrate the proposed approach. The results obtained by proposed approach are compared with the existing fuzzy Lambda–Tau and the crisp methodologies. 
Performance and behavior analysis of repairable industrial systems using Vague Lambda–Tau methodology