Incorporating expert knowledge in the estimation of parameters of the proportional hazards model.

摘要

The Proportional Hazards Model (PHM) has been applied widely in reliability and many other fields since the 1980s. To be effective, a PHM with time dependent covariates needs a lot of statistical data in a proper format. However, in reality, part or most of such data might not be available. This fact signifies the need for incorporation of other sources of knowledge and information such as experts' opinion when estimating the parameters of a PHM. Most of the current knowledge elicitation techniques usually take a lot of time and require the experts in the industry to be familiar with probability and statistics concepts and thus these techniques appear confusing and uninteresting to the experts. The main objective of this research is to establish a methodology that can utilize experts' knowledge and use it along with statistical data to estimate the parameters of a PHM without requiring the experts to be familiar with common concepts in probability and statistics. The main contributions of this research are:; First, the knowledge elicitation process developed in this research is easy to understand for people in industry because it is based on case analyses and comparisons. It is not difficult for an expert to compare different machine conditions in terms of probability of having a failure.; Second, a new knowledge elicitation protocol is developed in this thesis. In this new protocol, the answers to the questions result in a set of inequalities which in turn define a feasible space for the parameters of the PHM. By sampling from the feasible space an empirical prior distribution can be estimated. Therefore we can sample directly from the prior distribution of the parameters without imposing any parametric format on it. This method reflects the knowledge of experts in a better way compared to many conventional methods.; Third, a posterior distribution can be obtained directly from samples of prior distribution and likelihood of the statistical data using Bayes' rule. This minimizes approximation in the process.; The methodology developed in this thesis has been applied in a few experiments and in one real industrial case and has shown promising results.