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

Abbas Pak,Nayereh Bagheri Khoolenjani,Manoj Kumar Rastogi

doi:10.18187/pjsor.v15i2.2398

Abstract

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 Lindleyâ€™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.

Highlights

The bathtub-shaped model specified by the probability density functionf (z;, ) = z −1ez e (1−ez ), z > 0, > 0, [1]and survival functionS(z;, ) = e (1−ez ), z > 0, > 0, [2]was investigated by Chen (2000) as a new distribution useful to analyze lifetime data
By using upper record values, we have discussed on Bayesian estimation of stress-stregth reliability in multicomponent stress-strength bathtub-shaped model
Considering squared error, linex and general entropy loss functions, all the Bayes estimates were computed by assuming gamma priors on the parameters

Summary

Introduction

Was investigated by Chen (2000) as a new distribution useful to analyze lifetime data. Several authors have used different inference techniques to estimate the reliability parameter R based on various approaches and distributional assumptions on (X ,Y ). Makhdoom et al (2016) derived Bayesian estimates of the reliability in stress-strength models with power Lindley components. Inference on the reliability in MSS models when the stress and strength follow Weibull distribution is considered by Kizilaslan and Nadar (2015). Rao et al (2012,2014) conducted a series of studies to estimate the reliability of MSS models by assuming generalized exponential and Burr XII distributions for the components. Raqab et al (2018) considered estimation of the two-parameter bathtub-shaped distribution based on record data. Bayesian inference on reliability in a multicomponent stress-strength bathtub-shaped model based on record values and stress components are independent random variables distributed as bathtub-shaped model.

Maximum likelihood estimation

Bayesian analyses

Simulation study

Data Analysis

Conclusions