Statistical theory of reliability and life testing: probability models (International series in decision processes)

Barlow, Richard E.

Proschan, Frank

HOLT. RINEHART AND WINSTON

<p>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.</p>

Reliability and Decision Making

Business & Money

Spizzichino, Fabio

Claroti, C.A.

Economics

Chapman and Hall/CRC

Dedicated to Professor Z. W. Birnbaum. Reliability and Fault Tree Analysis. Theoretical and Applied Aspects of System Reliability and Safety Assessment

Science & Math

Mathematics

Society for Industrial & Applied

<p>This monograph presents a survey of mathematical models useful in solving reliability problems. It includes a detailed discussion of life distributions corresponding to wearout and their use in determining maintenance policies, and covers important topics such as the theory of increasing (decreasing) failure rate distributions, optimum maintenance policies, and the theory of coherent systems. The emphasis throughout the book is on making minimal assumptions - and only those based on plausible physical considerations - so that the resulting mathematical deductions may be safely made about a large variety of commonly occurring reliability situations. The first part of the book is concerned with component reliability, while the second part covers system reliability, including problems that are as important today as they were in the 1960s. The enduring relevance of the subject of reliability and the continuing demand for a graduate-level book on this topic are the driving forces behind its re-publication.</p>

Mathematical Theory of Reliability (Classics in Applied Mathematics, Series Number 17)

Society for Industrial and Applied Mathematics

Engineering reliability concerns failure data analysis, the economics of maintenance policies, and system reliability. This textbook develops the use of probability and statistics in engineering reliability and maintenance problems. The author uses probability models in the analysis of failure data, decisions relative to planned maintenance, and prediction relative to preliminary design. Some of the outstanding features include the analysis of failure data for both continuous and discrete probability from a finite population perspective, probability models derived from engineering considerations, an introduction to influence diagrams and decision making, and use of the operational Bayesian approach. The approach is fresh and interesting; it is motivated from problems in engineering and physical sciences and uses examples to illustrate the methodology. These examples, along with the use of real failure time data, will help the reader apply the techniques to real industrial situations.

Engineering Reliability (ASA-SIAM Series on Statistics and Applied Probability, Series Number 2)

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