Estimation of Reliability in Multicomponent Stress-strength Based on Generalized Exponential Distribution

A multicomponent system of k components having strengths following k independently and identically distributed random variables X-1, X-2, ... , X-k and each component experiencing a random stress Y is considered. The system is regarded as alive only if at least s out of k (s < k) strengths exceed the stress. The reliability of such a system is obtained when strength and stress variates are given by generalized exponential distribution with different shape parameters. The reliability is estimated using ML method of estimation in samples drawn from strength and stress distributions. The reliability estimators are compared asymptotically. The small sample comparison of the reliability estimates is made through Monte Carlo simulation. Using real data sets we illustrate the procedure.