Stress–strength reliability estimation involving paired observation with ties using bivariate exponentiated half-logistic model

ABSTRACT

This paper deals with the problem of maximum likelihood and Bayesian estimation of stress–strength reliability involving paired observation with ties using bivariate exponentiated half-logistic distribution. This problem is of importance because in some real applications the strength of the component is highly dependent on the stress experienced by it. A bivariate extension of exponentiated half-logistic is discussed and an expression for the stress–strength reliability is obtained. This model is also useful to analyse data having the unusual feature of having a number of pairs with tied scores, even when the scores are continuous. The maximum likelihood estimate and interval estimate of the stress–strength reliability has been developed. The Bayes estimates of the stress–strength reliability under squared error loss function are obtained using importance sampling technique. Simulation studies are conducted to evaluate the performance of maximum likelihood and Bayes estimates. Two real-life data sets are analysed to numerically illustrate the usefulness of the developed method.

Keywords:

• Bivariate exponentiated half-logistic model
• stress–strength reliability
• maximum likelihood estimates
• Bayesian estimation
• Markov chain Monte Carlo method
• ties

Acknowledgments

The authors are thankful to Dr. A. M. Mathai for his useful insights. The authors also thank the reviewers and the associate editor who helped in improving this paper.

Disclosure statement

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