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Parameter interval estimation of system reliability for repairable multistate series-parallel system with fuzzy data. (English) Zbl 1328.90033

Summary: 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 \(n \geq 100\). In addition, the optimal \(\ alpha \)-cut for the narrowest lower expected length and the narrowest upper expected length are considered.

MSC:

90B25 Reliability, availability, maintenance, inspection in operations research
62P20 Applications of statistics to economics
62N05 Reliability and life testing
62F10 Point estimation
62F86 Parametric inference and fuzziness
90C70 Fuzzy and other nonstochastic uncertainty mathematical programming

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