Estimation of stress-strength reliability R=P(X>Y) based on Weibull record data in the presence of inter-record times

Abstract

A considerable body of literature has been recently devoted to the inference problem of the reliability parameter R=P(X>Y) based on record data. In this article, we consider the records as well as the corresponding inter-record times to develop inference procedures for R assuming X and Y come from Weibull distribution. The maximum likelihood estimator of R and its corresponding confidence interval are determined. Bayesian analyses involving Tierney and Kadane’s approximation and Metropolis-Hasting samplers are used to estimate R based on LINEX and square error loss functions. In addition, the estimation problem of R is discussed in the models with known shape parameters. To compare all methods developed here, numerical simulation is carried out. Finally, different real data sets are analyzed.

Keywords

• Stress-strength model
• Bayesian method
• Inter-record times
• Records