Optimal Fuzzy Based Availability of Industrial System with Warm Standby Unit Subject to Partial Failure Effect and Common Cause Shock Failure
Nisha , Naveen Kumar, Nitin Tanwar
Abstract
This paper presents a comprehensive reliability and availability analysis of a machinery system consisting of
two operating units and one warm standby unit under fuzzy environment. The system is subject to partial failure
effects, rebooting mechanisms, repair rates, and common cause shock failures. Traditional crisp reliability
models often fail to capture the inherent uncertainties in system parameters such as failure rates, repair rates, and
shock intensities. By employing fuzzy set theory and triangular fuzzy numbers (TFNs), this study provides a
more realistic representation of system behavior under uncertainty. Mathematical models are developed using
Markov processes and supplementary variable technique, with fuzzy parameters incorporated through α-cut
methodology. Numerical examples demonstrate the impact of partial failures, rebooting efficiency, and common
cause shocks on system performance metrics. The results indicate that fuzzy reliability analysis provides
valuable insights for maintenance planning and system design optimization.
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