Semi-parametric hazard ratio applied to engineering insurance system

The objective of hazards (lifetime) analysis is to advance and promote statistical science in the various applied fields that deal with lifetime (survival) data including: actuarial science and reliability engineering. The lifetime data analysis provides special techniques that are required to compare the risks for failure. Bayesian semi-parametric methods have been applied to survival analysis problems since the emergence of the area of the Bayesian semi-parametric procedures. Cox proportional hazard model (PHM) estimates hazard ratios. Cox PHM is considered as constant hazard ratio over time if and only if Cox PHM assumptions are not violated. In Bayesian analysis, Markov Chin Monte Carlo (MCMC) methods have become a ubiquitous tool as the computer is more powerful. In this article, estimation of the parameters in Cox PHM is presented by using Bayes methods based on MCMC algorithm and duplicate the results using non-Bayes framework. The method is motivated by an example based on a hypothetical engineering insurance system.