Discusses the reasons which have motivated the changes in the mathematical technology of reliability theory, and gives readers an insight into the disciplines which recently started playing an important role in the reliability field.
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The very scope of reliability analyses is to take decisions relative to engineering systems. This commands for radical changes in the probabilistic/statistical techniques used in reliability practice. Since the decisions to be taken have an engineering/economical relevance (one can incur a loss if the system fails before mission time), the superimposed cost structure does play a central role in any reliability problem. Only the Bayesian predictive approach allows to combine harmonically together, costs and probabilities. Using a predictive approach means to assess one's own probability distribution on the observable random quantities of interest (for example, on the failure time of a system). The probability assessment is possibly made on the basis of some statistical evidence. In this view, parameters of probability distributions are just a computational aid to derive the probability of interest. From the Bayesian predictive standpoint, any reliability problem (even a system reliability problem) becomes a decision problem in face of uncertainty. Uncertainty can be mitigated by some forthcoming statistical evidence; the latter has, in general, a dynamic character.
It is often the case that one can exercise some control on the forthcoming information. First decisions to be taken when coping with a reliability problem is then: what course of actions will make the control on the forthcoming information optimal (in some suitable sense)? The need of answering this question and the dynamic character of the statistical evidence require the use of the theory of point process, of the theory of stochastic control and of the theory of stochastic filtering. The volume aims to enlighten the reasons which motivated the changes in the mathematical technology of reliability theory, and to give the readers an insight into the disciplines which recently started playing an important role in the reliability field. This volume should be of interest to both reliability theoreticians and practitioners.
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Summary
Reliability and Decision Making
Part 1 Fundamentals of statistical decision theory: decision making - drawbacks of the classical statistics approach; the likelihood principle in reliability analysis; Dutch books, the Jeffrey-Savage theory of hypothesis testing and Bayesian reliability; influence diagrams and decision modelling. Part 2 Sequential problems in reliability - a dynamical approach: concepts of optimality in stochastic control; information and reliability - a Bayesian perspective; multivariate conditional hazard rate and mean residual life functions and their applications; point processes and some application in reliability theory; a unifying model for the optimal design of life-testing and burn-in; on stochatic control concepts for sequential burn-in procedures. Part 3 Bayesian models in reliability and quality control: similarity as a probabilistic characteristic of ageing; shannon information, Bayesian design for prediction in accelerated life-testing; the Bayesian approach to quality; design by decision theory - a unifying perspective on Taguchis approach to quality engineering; some aspects of change-point problems. Part 4 Engineering reliability: modelling dependence in coherent systems; conservative Bayesian interval estimation of system reliability; the interpretation of probability, de Finetti's representation theorem and their implications to the use of expert opinions in safety assessment; making decision via PRA - the frequentist vs the Bayesian approach; using expert opinions in Bayesian estimation of system reliability.
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