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 (X 1,X 2,…,X k ) are strengths of k components subjected to a common stress (Y), then the reliability of the system or system reliability is given byR=P[Y<X (k−s+1)] whereX (k−s+1) is (k−s+1)-th order statistic of (X 1,…,X k ). We estimate R when (X 1,…,X k ) follow an absolutely continuous multivariate exponential (ACMVE) distribution of Hanagal (1993) which is the submodel of Block (1975) and Y follows an independent exponential distribution. We also obtain the asymptotic normal (AN) distribution of the proposed estimator.
Key words and PhrasesAbsolutely continuous multivariate exponential model Maximum likelihood estimate S-out-of-K system Stress-Strength model System reliability
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