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System reliability for non-repairable multi-state series-parallel system using fuzzy Bayesian inference based on prior interval probabilities. (English) Zbl 1342.60152

Summary: In this article, fuzzy concepts are applied in the analysis of a system reliability problem. Fuzzy numbers are used to construct the fuzzy reliability of a non-repairable multi-state series-parallel system (NMSS). The fuzzy failure rate function is represented by an exponential fuzzy number. By using this innovative approach, the fuzzy system reliability of an NMSS is created. In order to analyse this fuzzy system reliability, a fuzzy Bayesian point estimation of the fuzzy system reliability is carried out by the conventional Bayesian formula, and the posterior fuzzy system reliability of an NMSS is developed by Bayesian inference with fuzzy probabilities. Finally, the performance of the method is measured by the mean square error of fuzzy Bayesian point estimateion for the fuzzy system reliability of the NMSS.

MSC:

60K10 Applications of renewal theory (reliability, demand theory, etc.)
62F15 Bayesian inference
60A86 Fuzzy probability
60J99 Markov processes
90B25 Reliability, availability, maintenance, inspection in operations research
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