Bayesian analysis using covariate information: A case study in reliability

An in-depth Bayesian analysis of two real life reliability problems is performed: an assessment of the reliability of machine tools under varying operating environments and the effect of the practice of rail grinding on the reliability of railroad tracks. In each case, the inclusion of covariate information is critical to the analysis. The proportional hazards model (PHM) and proportional intensities model (PIM) were introduced to include covariate information in failure models.; The PHM is used to model the effect of the operating environment on machine tools. Bayesian analysis of the PHM has been previously performed under a parametric assumption. In the machine tool application this assumption is considered too restrictive and therefore a semi-parametric analysis is presented using a mixture of Dirichlet processes (MDP) approach. This approach relaxes the parametric assumption and allows an investigation of whether the set of covariates used in the analysis completely explain the differences between the machine tools. A comparison via Bayes Factors is used to demonstrate that the MDP approach gives better predictive estimates than a parametric model. Optimal replacement intervals are obtained for individual machine tools under the age replacement protocol and for groups of machine tools with diverse operational environments under the block replacement protocol.; The PIM is used to model the effect of the practice of grinding on a rail section's reliability. Other physical characteristics and operational uses of the rail needed to be included in the analysis to determine the actual effect of grinding. Parametric and two semi-parametric analyses of the PIM are developed. The first semi-parametric approach is based on a gamma process prior. The complexity of the analysis under this assumption, due to the nature of the data, is demonstrated. To overcome these problems, a second semi-parametric approach using a MDP set-up is used. The MDP set-up allows the investigation of whether there are other covariates that could be included to improve the analysis. Optimal replacement intervals are developed for groups of rails with different physical characteristics and maintenance policies under the block replacement protocol. The effect of rail grinding on the replacement interval of a section of rail is investigated.