Prior Elicitation and Evaluation of Imprecise Judgements for Bayesian Analysis of System Reliability

System reliability assessment is a critical task for design engineers. Identifying the least reliable components within a to-be system would immensely assist the engineers to improve designs. This represents a pertinent example of data-informed decision-making (DIDM). In this chapter, we have looked into the theoretical frameworks and the underlying structure of system reliability assessment using prior elicitation and analysis of imprecise judgements. We consider the issue of imprecision in the expert’s probability assessments. We particularly examine how imprecise assessments would lead to uncertainty. It is crucial to investigate and assess this uncertainty. Such an assessment would lead to a more realistic representation of the expert’s beliefs, and would avoid artificially precise inferences. In other words, in many of the existing elicitation methods, it cannot be claimed that the resulting distribution perfectly describes the expert’s beliefs. In this paper, we examine suitable ways of modelling the imprecision in the expert’s probability assessments. We would also discuss the level of uncertainty that we might have about an expert’s density function following an elicitation. Our method to elicit an expert’s density function is nonparametric (using Gaussian Process emulators), as introduced by Oakley and O’Hagan [1]. We will modify this method by including the imprecision in any elicited probability judgement. It should be noticed that modelling imprecision does not have any impact on the expert’s true density function, and it only affects the analyst’s uncertainty about the unknown quantity of interest. We will compare our method with the method proposed in [2] using the ‘roulette method’. We quantify the uncertainty of their density function, given the fact that the expert has only specified a limited number of probability judgements, and that these judgements are forced to be rounded. We will investigate the advantages of these methods against each other. Finally, we employ the proposed methods in this paper to examine the uncertainty about the prior density functions of the power law model’s parameters elicited based on the imprecise judgements and how this uncertainty might affect our final inference