Estimation of reliability function and mean time to system failure for k-oYut-of-n systems using Weibull failure time model

The objective of this paper is to estimate the reliability function and mean time to system failure of a k-out-of-n system which consists of n independent and identically distributed components with life times following Weibull model. The system is operational until at least k of its n components are functional. The Reliability characteristics are obtained using uncensored failure observations by both the maximum likelihood estimation and Bayesian methods. The Bayes estimates are obtained using Lindley's approximation technique with non-informative and informative priors under squared error loss function. The asymptotic confidence interval is constructed for the reliability function using maximum likelihood estimator. A simulation study is carried out for comparing the performances of these estimates with respect to their mean squared errors. Analysis of a real data set is also given.