Introduction to Imprecise Probabilities

Chapter 14Reliability and risk

Frank P. A. Coolen¹ and Lev V. Utkin²

¹Department of Mathematical Sciences, Durham University, UK

²Department of Control, Automation and System Analysis, Saint-Petersburg State Forest Technical University, Russia

14.1 Introduction

Reliability and risk analysis are important application areas of statistics and probability theory in engineering and related fields, with several specific features which often complicate application of standard methods. Such features include data censoring, lack of knowledge and information on dependence between random quantities, and required use of expert judgements. These may, for example, result from the use of new or upgraded systems, multiple failure modes and maintenance activities. While mathematical approaches for dealing with such issues have been presented within the framework of statistics using precise probabilities, the use of imprecise probabilities provides exciting new ways for dealing with such challenges in reliability and risk. Attractive features of imprecise probability theory for this application area include the ability to model and reflect partial information about random quantities or the dependence of these and the ability to take expert judgement into account in a realistic way when only limited elicitation is possible due to time constraints. All kinds of partial information that might be available in practice can be formulated as constraints which have to be satisfied by sets of probabilities, ...