Estimation of reliability in multicomponent stress-strength model: Log-logistic distribution

Abstract

A multicomponent system of k components having strengths following k- independently and identically distributed random variables x₁, x₂, ....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, stress variates are given by log-logistic distribution with different scale parameters. The reliability is estimated using Moment Method, ML method, Modified ML method and Best Linear Unbiased 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.