This paper is a state-of-the-art review of the literature related to optimal maintenance models of systems subject to failure. The emphasis is on work appearing since the 1976 survey, “A Survey of Maintenance Models: The Control and Surveillance of Deteriorating Systems,” by W.P. Pierskalla and J.A. Voelker, published in this journal.

Optimal maintenance models for systems subject to failure–A Review

A survey of the search theory literature

A collection of papers on the application of Markov decision processes is surveyed and classified according to the use of real life data, structural results and special computational schemes. Observations are made about various features of the applications.

A Survey of Applications of Markov Decision Processes

DYNAMI C programming, a mathematical field that has grown up in the past few years, is recognized in the U.S.A. as an important new research tool. However, in other countries, little interest has as yet been taken in the subject, nor has much research been performed. The objective of this paper is to give an expository introduction to the field, and give an indication of the variety of actual and possible areas of application, including actuarial theory. In the last decade a large amount of research has been performed by a small body of mathematicians, most of them members of the staff of the RAND Corporation, in the field of multi-stage decision processes, and during this time the theory and practice of the art have experienced great advances. The leading force in these advances has been Richard Bellman, whose contributions to the subject, which he has entitled Dynamic Programming(I), have had effects not only in immediate fields of application but also in general mathematical theory; for example, the calculus of variations (see chapter IX of (I)), and linear programming (chapter VI). The work done so far has paved the way for innumerable further research and applications, and hence the field, besides being a very stimulating one, is one which new blood will find potentially highly fruitful. As will be seen when the concept of dynamic programming is defined and illustrated more fully below, a further development in the last decade that has made research in the subject more feasible and useful has been the evolution of the digital computer, which has made it possible to simulate complicated processes and hence deduce their properties by Monte Carlo methods; sometimes,

An introduction to dynamic programming

Y TASK of preparing a survey of search theory has been eased by having access to two bibliographies. ENSLOW[81 t has prepared a bibliography, with abstracts, of Search Theory and Reconnaissance Theory that partially serves the purpose of a survey. S. M. POLLOCK has prepared a selected bibliography, while teaching a course on Search, Detection, and Reconnaissance at the U. S. Naval Postgraduate School in Monterey, and has kindly given me a copy. Each list contains approximately 70 entries, after eliminating duplications (same author and almost identical paper) from Enslow's list. The intersection of the two sets is surprisingly small, consisting of less than half the elements in one set, and amounting to about 30 per cent of the (distinct) elements in the union of the two sets. Pollock lists 14 papers in Detection Theory that are concerned primarily with the functioning of the detecting instrument, a subject not covered in Enslow's bibliography. It is evident from the subheadings in the two lists that there is a large difference in emphasis. Also, it is evident from the entries that the marginal sources available to the two men were quite different. There are 10 to 30 additional papers known to me (and, no doubt, many other papers not known to me) that can be added to the combined list, the number depending on the criterion for inclusion. However, it is not my intention to compile a comprehensive bibliography. My purpose here is to survey a part of the field of Search: the part, known as Search Theory, that is concerned with the question of how to conduct a search to achieve a stated objective. For this purpose I have compiled a selected bibliography, with the papers grouped and ordered for convenience in making the survey. No definite criterion was used in making selections, except for the requirement that the paper make a contribution to the development. The numbering used below is the same as the numbering used in the bibliography. The theory is emphasized almost to the point of excluding applications,

A Survey of Search Theory

Consider a complex system consisting of N modules containing n(1), …, n(N) items or sub-circuits. A very simple device of this nature, for example, would be a hi-fi set, where the amplifier, the cartridge, the speaker(s) and the turntable could be considered to be the modules, and the various parts of each as the basic items in which faults could occur. A more realistic application of the results obtained might be to a radar-missile system, in which surveillance radar, tracking radar, communications system, computer, missile launcher and missile, or parts of them, represent the modules. When the system breaks down, the procedure for detecting the breakdown and hence repairing the system will determine the time taken to repair it. Assuming two different possible models, equations are developed for the optimum policy, i.e., the policy which minimizes the expected amount of time consumed or penalties paid, and these equations are solved for the first model. Model I assumes that over-all tests of each module ...

Brian Gluss

Papers

An Optimum Policy for Detecting a Fault in a Complex System