A pythagorean fuzzy approach to consecutive k-out-of-r-from-n system reliability modelling

The linear consecutive (LC) k-out-of-r-from-n system is an incredibly important configuration used in various engineering systems. Such a system will break down if at least k out of r consecutive elements become inoperable in a system consisting of n ordered components. For any system, the critical necessity is that it should be reliable and remain in a properly functioning state for a stipulated period of time, thus, making it necessary to evaluate the reliability of such systems as well. However, the conventional reliability evaluation methods fail to consider the fuzziness or prospect of errors while computing the reliability, which can be resolved by incorporating fuzzy theory. This particular work presents a novel method for the computation of fuzzy reliability and its sensitivity for an LC k-out-of-r-from-n system, where its inherent fuzziness is addressed with the help of Pythagorean fuzzy sets (PFS), by representing the fuzzy variables as a trapezoidal Pythagorean fuzzy number (TrPFN), due to its ability to consider both membership and non-membership values, unlike the traditional fuzzy sets. Moreover, the universal generating function (UGF) technique is used to obtain the reliability function. Further, two different distributions are considered to represent the failure rates, namely, the Weibull and Pareto distributions and it was established that the Pareto distribution yields better results than the Weibull distribution. The obtained results are then compared with the help of both tabular and graphical illustrations.