Abstract
The purpose of this paper is to create an interval estimation of the fuzzy system reliability for the repairable multistate series–parallel system (RMSS). Two-sided fuzzy confidence interval for the fuzzy system reliability is constructed. The performance of fuzzy confidence interval is considered based on the coverage probability and the expected length. In order to obtain the fuzzy system reliability, the fuzzy sets theory is applied to the system reliability problem when dealing with uncertainties in the RMSS. The fuzzy number with a triangular membership function is used for constructing the fuzzy failure rate and the fuzzy repair rate in the fuzzy reliability for the RMSS. The result shows that the good interval estimator for the fuzzy confidence interval is the obtained coverage probabilities the expected confidence coefficient with the narrowest expected length. The model presented herein is an effective estimation method when the sample size is n ≥ 100. In addition, the optimal α-cut for the narrowest lower expected length and the narrowest upper expected length are considered.
Highlights
Most researches on reliability theory involve traditional binary reliability models where each component in a system basically consists of two functional states, perfect functionality and complete failure
Some studies showed that much research proposed an approach based on fuzzy data for constructing a fuzzy confidence interval, but without considering the performance analysis of interval estimator
The performance of fuzzy confidence interval is assessed based on the coverage probability and the expected length
Summary
Most researches on reliability theory involve traditional binary reliability models where each component in a system basically consists of two functional states, perfect functionality and complete failure. In the system reliability of multistate components, the entire system performance will be considered from different performance levels and several failure modes. The evolution of such a system is represented by a continuous-time discrete state stochastic process. The inaccuracy of system models, caused by human errors, is difficult to quantify using conventional reliability theory alone [9]. In light of these significant challenges, new techniques are needed to solve these fundamental problems related to reliability
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