Fuzzy Reliability Evaluation of Complex Systems Using Intuitionistic Fuzzy Sets

Introduction

Reliability is one of the most important characteristics of any system. When faced with an unusual failure mode, we need to learn what is causing the failure in order to solve the problem. To solve all these kinds of problems reliability modelling and assessment are critical for pursuing high reliability or availability level. In the real-world problem, the data or the system parameters are often imprecise and for conventional reliability analysis use of probabilistic approach is inadequate. Therefore, IFS technique is introduced to analyse the reliability of a complex system.

In context of UGF technique, Levitin et al. (2000) solved the redundancy optimization problem for power systems using genetic algorithms (GA), where the elements of the system had different capacities. Also, UGF method was used to estimate the reliability of multi-state power system with series-parallel structure. Levitin and Lisnianski (2001) presented a new technique for reliability optimization problems for the family of multistate system. Authors combined UGF for quick reliability evaluation and GA for optimization. Levitin (2002) had used modified UGF technique on correct classification probability of weighted voting classifiers. Author suggested a method to make the classification decisions with both plurality and threshold voting without imposing constraints on unit weights. Levitin (2005) proposed a new multi-state model of linear consecutive k-out-of-r-from-n: F system with multiple failure criteria and calculated the reliability of the proposed system with the help of UGF technique. Lisnianski and Ding (2009) proposed a redundant model that is typically in a multi-state system. Authors had considered two interconnected multi-state systems where one of them was a redundant system and calculated the reliability of the considered system using UGF and random process methods. Ding et al. (2010) studied the impact of high wind power on the windmill for long term planning point of view. In the model windmill and conventional generators were combined and the reliability of the system was evaluated with the help of UGF technique. Yingkui and Jing (2012) presented a systematic review on the reliability evaluation of multi-state systems. Authors also summarized optimization and maintenance of the complex multi-state system. Tillman et al. (1970) considered a complex system and estimated it’s reliability using Bayes theorem and then the reliability of the system was optimized with the help of sequential unconstrained minimization technique.

Binary state assumption in probist (i.e., conventional) reliability theory has shown earlier. This Concept of presenting a system completely failed or working was not extensively acceptable, and thus binary state assumption were replaced by the fuzzy state. Cai et al. (1993) introduced the conceptual framework of profust reliability which was developed based on the fuzzy state assumption and probability assumption. Cheng and Mon (1993) proposed a more general and simplified approach of evaluating fuzzy system reliability by arithmetic and α- cuts interval. Jiang and Chen (2003) has given a numerical algorithm to compute fuzzy reliability of systems such as mechanical components, sensors, electronic units etc. This algorithm grounds the reliability analysis of the system where components are with fuzzy reliability. Wu (2004) proposed the Bayesian reliability estimation under fuzzy environment. Invoking the Resolution Identity theorem fuzzy Bayes point estimation was created. Fuzzy reliability for series and parallel systems using intuitionistic fuzzy set theory was analysed with a new developed approach by Kumar et al. (2011). Authors introduced trapezoidal intuitionistic fuzzy set number and arithmetic operations between two trapezoidal intuitionistic fuzzy set numbers. Authors have also shown that triangular intuitionistic fuzzy set number is a special case of trapezoidal intuitionistic fuzzy set number. Garg et al. (2014) presented multi-objective reliability optimization methodology with triangular interval data. Authors resolved a conflict between the objectives with the help of intuitionistic fuzzy programming technique. Kumar and Ram (2018 & 2019) evaluated the fuzzy reliability of binary and complex system on the basis of hesitant and dual hesitant fuzzy set theory using Weibull distribution and recursive methods. Kumar et al. (2019) discussed the fuzzy reliability of complex system having dissimilar components with IFS theory, Weibull distribution and Markov process techniques.