Reliability analysis of repairable systems using Petri nets and vague Lambda-Tau methodology

The main objective of the paper is to developed a methodology, named as vague Lambda-Tau, for reliability analysis of repairable systems. Petri net tool is applied to represent the asynchronous and concurrent processing of the system instead of fault tree analysis. To enhance the relevance of the reliability study, vague set theory is used for representing the failure rate and repair times instead of classical(crisp) or fuzzy set theory because vague 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. The proposed methodology involves qualitative modeling using PN and quantitative analysis using Lambda-Tau method of solution with the basic events represented by intuitionistic fuzzy numbers of triangular membership functions. Sensitivity analysis has also been performed and the effects on system MTBF are addressed. The methodology improves the shortcomings of the existing probabilistic approaches and gives a better understanding of the system behavior through its graphical representation. The washing unit of a paper mill situated in a northern part of India, producing approximately 200 ton of paper per day, has been considered to demonstrate the proposed approach. The results may be helpful for the plant personnel for analyzing the systems' behavior and to improve their performance by adopting suitable maintenance strategies.