MCMC for Inference on Phase-type and Masked System Lifetime Models

Commonly reliability data consist of lifetimes (or censoring information) on all components and systems under examination. However, masked system lifetime data represents an important class of problems where the information available for statistical analysis is more limited: one only has failure times for the system as a whole, but no data on the component lifetimes directly, or even which components had failed. For example, such data can arise when system autopsy is impractical or cost prohibitive. The problem of statistical inference with such masked system lifetime data is considered in the situation where component repair is and is not possible. Continuous-time Markov chains are widely-used models for repairable systems with redundancy, with an absorbing state representing failure. The failure time is then the first passage time to the absorbing state, which is modelled by a Phase-type distribution. Bayesian inference via MCMC for Phase-type distributions when data consist only of absorption times is considered. Extensions to the existing methodology of Bladt et al. (2003) are presented which accommodate censored data, enable a structure to be imposed on the underlying continuous-time Markov process and expand computational tractability to a wider class of situations. This part of the research is also broadly applicable outside the reliability interpretation presented in this thesis. For non-repairable systems, a novel signature based data augmentation scheme is presented which enables inference for a wide class of component lifetime models for an exchangeable population of systems. It is shown that the approach can be extended to enable topological inference of the underlying system design. Finally, two R packages (‘PhaseType’ and ‘ReliabilityTheory’) are provided which enable reliability practitioners to make use of the theoretical contributions of this research easily.