Application of picture fuzzy set theory to reliability and risk analysis of complex industrial systems

In the present study, a novel methodology named “Picture Fuzzy Lambda-Tau Methodology (PFLTM)” is developed for the reliability and risk analysis of complex systems in uncertain and fuzzy environments. The methodology obtained is helpful for both qualitative and quantitative analyses of complex systems. In qualitative analysis, the Petri Net (PN) Model is developed from the corresponding fault tree. Whereas, in quantitative analysis, picture fuzzy set theory is combined with the lambda-tau methodology to get the membership function of reliability parameters. Additionally, a new method for risk analysis is developed to address the limitations of conventional risk analysis methods. The washing unit of a paper mill has been considered to exhibit the proposed methodology. Various expressions of reliability measures of the system, like mean time to repair (MTTR), mean time between failures (MTBF), reliability, availability, and expected number of failures (ENOFs), are obtained. Also, for different spreads, the numerical values of these measures are calculated and compared with different existing methodologies.