Availability and Reliability Analysis of a k-Out-of-n Warm Standby System with Common-Cause Failure and Fuzzy Failure and Repair Rates

In the real life, there exists limited information or uncertainty in knowledge about failure and repair rates which follow one of the standard distributions as exponential distribution and Weibull distribution with some parameters. We suppose that these parameters are fuzzy which allow one to specify a system design for a "worst-case scenario."In this paper, the fuzzy availability and the fuzzy reliability of a redundant repairable parallel k-out-of-n warm standby system with common-cause failure are evaluated. We assume that the failure time of each operating unit or warm standby unit follows Weibull distribution with two fuzzy parameters and the repair time of any failed unit follows exponential distribution with one fuzzy parameter. Each fuzzy parameter is represented by triangular membership function estimated from statistical data taken from random samples of each unit. Also, we give a numerical example for a fuzzy repairable parallel 3-out-of-5 warm standby system with two active and three warm standby units to get analytically and represent graphically the fuzzy availability and reliability function of this fuzzy system.