Inference on stress–strength reliability for exponential distributions with a common scale parameter

ABSTRACT

This paper considers estimation of the stress–strength reliability when the stress and strength follow two-parameter exponential distributions having different location parameters and a common scale parameter. All parameters are assumed to be unknown. We derive the uniformly minimum variance unbiased estimator, Bayes estimators and an affine equivariant estimator of the stress–strength reliability. We propose confidence intervals of the stress–strength reliability based on the generalized variable approach and percentile bootstrap method. We also derive an approximate confidence interval and Bayesian intervals of the reliability parameter. Numerical comparisons among the proposed estimators are carried out using intensive simulations. Illustrative examples have been given using real data sets.

KEYWORDS:

• Bayes estimator
• best scale equivariant estimator
• generalized pivot variable
• maximum likelihood estimator
• stress–strength model
• uniformly minimum variance unbiased estimator

Acknowledgments

The authors express sincere gratitude to the reviewers, Associate Editor and Editor for their valuable comments which led to the substantial improvement of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.