Parameter Estimates of General Failure Rate Model: A Bayesian Approach

TL;DR

This paper develops Bayesian parameter estimates for a general failure rate model, considering dependence between parameters and using various loss functions to improve reliability analysis accuracy.

Contribution

It introduces Bayesian estimation methods for the failure rate model with dependent parameters, extending previous work that assumed independence.

Findings

Derived Bayesian estimates under squared error, linex, and entropy loss functions.

Analyzed the impact of parameter dependence on estimation accuracy.

Provided a comprehensive framework for reliability modeling with dependent parameters.

Abstract

The failure rate function plays an important role in studying the lifetime distributions in reliability theory and life testing models. A study of the general failure rate model $r(t)=a+bt^{\theta-1}$, under squared error loss function taking $a$ and $b$ independent exponential random variables has been analyzed in the literature. In this article, we consider $a$ and $b$ not necessarily independent. The estimates of the parameters $a$ and $b$ under squared error loss, linex loss and entropy loss functions are obtained here.