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

Abstract

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.

Keywords:

• Bayes estimators
• maximum likelihood estimator
• percentage risk improvement
• stress–strength reliability
• uniformly minimum variance unbiased estimator

AMS Classifications:

• 62N05
• 62F10

Acknowledgments

We thank the editor-in-chief and an associate editor for their valuable suggestions which have led to substantial improvement in the content and presentation of the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).