ESTIMATION OF SYSTEM RELIABILITY IN AN S-OUT-OF-K SYSTEM

In this paper, we estimate the reliability of a system with k components. The system functions when at least s (1 ≤ s ≤ k) components survive a common random stress. We assume that the strengths of these k components are subjected to a common stress which is independent of the strengths of these k components. If (X1, X2,..., Xk) are strengths of k components subjected to a com-mon stress (Y), then the reliability of the system or system reliabil-ity is given by R = P [Y < X(k−s+1)] where X(k−s+1) is (k-s+1)-th order statistic of (X1,..., Xk). We estimate R when (X1,..., Xk) fol-low an absolutely continuous multivariate exponential (ACMVE) distribution of Hanagal(1993) which is the submodel of Block(1975) 1 and Y follows an independent exponential distribution. We also obtain the asymptotic normal(AN) distribution of the proposed es-timator. Key words and Phrases: Absolutely continuous multivariate ex-ponential model, Maximum likelihood estimate, S-out-of-K system