Abstract
The estimation of the reliability of a series system of k(≥ 2) independent components, where the life time of each component is exponentially distributed, has been considered. First, sufficient conditions for obtaining improvements over scale equivariant estimators for the one-parametric model are derived. As a consequence, we derive estimators that improve upon the maximum likelihood estimator (MLE), an analog of the uniformly minimum variance unbiased estimator (UMVUE) and the best-scale equivariant estimator (BSEE). Bayes and generalized Bayes estimators are also obtained and are shown to be admissible. We consider also the case where the lifetimes follow two-parametric exponential distributions and derive the UMVUE of the system reliability. Further, the MLE and the modified MLE (MMLE) are discussed for this case. Finally, the risks of these estimators are compared numerically for the case k = 2.
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