On Reliability in a Multicomponent Stress-Strength Generalized Rayleigh Model Based on Record Values

Abstract

Abstract In the literature, there are well-developed estimation techniques that can be used to measure the reliability in multicomponent stress-strength models when the information about all experimental units are available. However, in real applications, only observations that exceed (or fall below) the current value may be recorded. In this article, assuming that the components of the system follow generalized Rayleigh distribution, we investigate classical and Bayesian estimation of the reliability of a multicomponent stress-strength model when the available data are reported in terms of record values. The maximum likelihood estimate of the reliability parameter and its asymptotic confidence interval are obtained. Moreover, two confidence intervals based on the parametric bootstrap methods are presented. The Bayes estimate of the reliability parameter is derived using different loss functions. Because there is no closed form for the Bayes estimate, we use the Markov chain Monte Carlo method to obtain an approximate Bayes estimate and the highest posterior density credible interval of the reliability. To evaluate the performances of different procedures, simulation studies are conducted, and an example of real data sets is provided.