Bayes approach to explore the mixture failure rate model.

Abstract

This thesis has two folds: Firstly, designing mixture failure rate functions by combing few other existing failure rate functions to obtain desirable mixture failure rate functions. The first proposed mixture failure rate is the non-linear failure rate. This failure rate is a mixture of the exponential and Weibull failure rate functions. It was designed for modeling data sets in which failures result from both random shock and wear out or modeling a series system with two components, where one component follows an exponential distribution and the other follows a Weibull distribution. The second proposed mixture failure rate is the additive Chen-Weibull failure rate. This failure rate is considered a mixture of the Chen and Weibull failure rates. It is decided for modeling lifetime data with flexible failure rate including bathtub-shaped failure rate. The final proposed mixture failure rate is the improvement of new modified Weibull failure rate. This failure rate is a mixture of the Weibull and modified Weibull failure rates. It is also decided for modeling lifetime data with flexible failure rate including bathtub-shaped failure rate. The superiority of the proposed models have been demonstrated by fitting to many well-known lifetime data sets. And secondly, applying modern statistical methods and techniques, such as the maximum likelihood estimation, Bayesian inference, cross-entropy method, adaptive Markov chain Monte Carlo, Hamiltonian Monte Carlo and bootstrapping, for analyzing failure time distributions which result from those mixture failure rate functions.