Bayesian inference on reliability in a multicomponent stress-strength bathtub-shaped model based on record values

In the literature, there are a well-developed estimation techniques for the reliability assessment in multicomponent stress-strength models when the information about all the experimental units are available. However, in real applications, only observations that exceed (or fall below) the current value may be recorded. In this paper, assuming that the components of the system follow bathtub-shaped distribution, we investigate Bayesian estimation of the reliability of a multicomponent stress-strength system when the available data are reported in terms of record values. Considering squared error, linex and entropy loss functions, various Bayes estimates of the reliability are derived. Because there are not closed forms for the Bayes estimates, we will use Lindley's method to calculate the approximate Bayes estimates. Further, for comparison purposes, the maximum likelihood estimate of the reliability parameter is obtained. Finally, simulation studies are conducted in order to evaluate the performances of the proposed procedures and analysis of real data sets is provided.