Estimation of System Reliability in Multi- Component Series Stress-strength Models

In this paper, we estimate the reliability of series system with k components. We assume the strengths of these k components are subjected to a common stress which is independent of the strengths of the k components. If (X1, ..., Xk) are strengths of k components subjected to a common stress Xk+1, then the reliability of the series system or system reliability (R) is given by R = P [Xk+1 < Min(X1, ..., Xk)]. We estimate R when (X1, ..., Xk+1) follow (k+1) independent Gamma, Weibull and Pareto distributions. We also obtain the asymptotic normal(AN) distributions of these estimates.