Estimation of Reliability in a Multicomponent Stress-Strength System for the Exponentiated Moment-Based Exponential Distribution

A multicomponent system of k components with independent and identically distributed random strengths X1,X2, horizontal ellipsis Xk, with each component undergoing random stress, is in working condition if and only if at least s out of k strengths exceed the subjected stress. Reliability is measured while strength and stress are obtained through a process following an exponentiated moment-based exponential distribution with different shape parameters. Reliability is gauged from the samples using maximum likelihood (ML) on the computed distributions of strength and stress. Asymptotic estimates of reliability are compared using Monte Carlo simulation. Application to forest data and to breaking strengths of jute fiber shows the usefulness of the model.