Estimating a new stress–strength index for several exponential populations with a common location

In design and development of products in various industries, a key characteristic is stress–strength reliability. In this article, we consider estimation of a new stress–strength index for several exponential populations with a common location. We derive various estimators such as the maximum likelihood, the uniformly minimum variance unbiased (UMVU), and Bayes estimators. We additionally apply Brewster–Zidek technique for improving upon estimators based on UMVU or best affine equivariant estimators of scale parameters. We derive the asymptotic distribution of the ML estimator and prove that the Bayes estimators' limit under a suitable prior distribution is a generalized Bayes estimator. We then evaluate the risk performance of the obtained estimators in an extensive simulation study. Two applications are given on real data sets to illustrate the new methods. One example relates to the duration analysis and the other to a problem of comparing strengths of different fibres in jute industry.