A sequential bayes procedure for reliability demonstration

A common problem in life testing is to demonstrate that the mean time to failure, θ, exceeds some minimum acceptable value, say θ₁, with a given confidence coefficient γ. When this is true, it is said that “θ₁ has been demonstrated with a confidence γ”. In this paper a Sequential Bayes Procedure (SBP) for demonstrating (by means of. a probability statement) that θ exceeds θ₁ is presented. The SBP differs from the classical procedure in the sense that a prior distribution is assumed on the parameter θ, calling for a Bayesian approach. The procedure is based on the sequence of statistics.     

Interception in a network

This paper presents an algorithm for determining where to place intercepting units in order to maximize the probability of preventing an opposing force from proceeding from one particular node in an undirected network to another. The usual gaming assumptions are invoked; namely, the strategy for placing the units is known to the opponent and he will choose a path through the network which, based on this knowledge, maximizes his probability of successful traverse. As given quantities, the model requires a list of the arcs and nodes of the network, the number of intercepting units available to stop the opposing force, and the probabilities for stopping the opposition at the arcs and nodes as functions of the number of intercepting units placed there. From these quantities, the algorithm calculates the probabilities for placing the unit at the arcs and nodes when one intercepting unit is available, and the expected numbers of units to place at the arcs and nodes when multiple intercepting units are available.     

Book reviews

Third World Military Expenditure: Determinants and Implications. By Robert McKinlay. Frances Pinter, London (1989)

The UK Defence Industrial Base: Development and Future Policy Options. By Trevor Taylor and Keith Hayward. Brassey's, London, for Royal United Services Institute (1989), ISBN 0-08-036713-5, £22.50

Mutiny. By Lawrence James. Buchan & Enright, London (1987), ISBN 0-907675-70-0, £12.95; Scapegoat! Famous Courts Martial. By John Harris. Severn House, London (1988), ISBN 0-7278-2103-2, £12.95; In Glass Houses. By Robert Boyes. Military Provost Staff Corps Association, Colchester (1986), ISBN 0-9513467-0-9, £6.50 (paperback)

The Nuclear Weapons World: Who, How and Where. Edited by Patrick Burke. Frances Pinter, London (1988), ISBN 086187-705-5, £50.00

Merchants of Treason—America's Secrets for Sale. By Thomas B. Allen and Norman Polmar. Robert Hale, London (1988), ISBN 0-7090-3543-8, £14.95 ($21.95); Intelligence and Intelligence Policy in a Democratic Society. Edited by Stephen J. Cimbala. Transnational Publishers, Dobbs Ferry, NY (1987), ISBN 0-941320-44-8, $37.50; Catching Spies—Principles and Practices of Counterespionage. By H. H. A. Cooper and Lawrence J. Redlinger. Paladin Press, Boulder, CO (1988), ISBN 0-87364-466-2, $24.95

The BattleshipRoyal Sovereignand Her Sister Ships. By Peter C. Smith. William Kimber, Wellingborough (1988), ISBN 0-7183-0704-6, £12.95; Air Power at Sea, 1945 to Today. By John Winton. Sidgwick & Jackson, London (1987), £9.95     

Book reviews

British Military History: a Supplement to Robin Higham's Guide to the Sources.. Edited by Gerald Jordan. Garland, New York (1988), xii + 586 pp., $75.00

Red Duster at War. By John Slader. William Kimber, London (1988), 352 pp., £15.50

Armed Services and Society. By Martin Edmonds. Leicester University Press, Leicester (1988), 226 pp., £25.00     

Properties of an approximate hazard transform

The calculation of the exact reliability of complex systems is a difficult and tedious task. Consequently simple approximating techniques have great practical value. The hazard transform of a system is an invertible transformation of its reliability function which is convenient and useful in both applied and theoretical reliability work. A simple calculus for finding an approximate hazard transform for systems formed by series and parallel combinations of components is extended so that it can be used for any coherent system. The extended calculus is shown to lead to conservative approximations. A first order version of the extended calculus is also discussed. This method of approximation is even more simple to use, but is not always conservative. Examples of its application indicate that it is capable of giving quite accurate results.     

Inference from accelerated life tests using eyring type re-parameterizations

Least squares estimators of the parameters of the generalized Eyring Model are obtained by using data from censored life tests conducted at several accelerated environments. These estimators are obtained after establishing that the Gauss-Markov conditions for least squares estimation are satisfied. Confidence intervals for the hazard rate at use conditions are obtained after empirically showing that the logarithm of the estimate of the hazard rate at use conditions is approximately normally distributed. The coverage probabilities of the confidence intervals are also verified by a Monte Carlo experiment. The techniques are illustrated by an application to some real data.     

Computerized scheduling of seagoing tankers

Computerized Scheduling of Seagoing Tankers The tanker scheduling problem considered in this paper is that of the Defense Fuel Supply Center (DFSC) and the Military Sealift Command (MSC) in the worldwide distribution of bulk petroleum products. Routes and cargoes which meet delivery schedule dates for a multiplicity of product requirements at minimum cost are to be determined for a fleet of tankers. A general mathematical programming model is presented, and then a mixed integer model is developed which attempts to reflect the true scheduling task of DFSC and MSC as closely as possible. The problem is kept to within a workable size by the systematic construction of a set of tanker routes which does not contain many possible routes that can be judged unacceptable from practical considerations alone.     

Spares stocking policies for repairable items with dependent repair times

This paper analyzes the problem of determining desirable spares inventory levels for repairable items with dependent repair times. The problem is important for repairable products such as aircraft engines which can have very large investment in spares inventory levels. While existing models can be used to determine optimal inventory spares levels when repair times are independent, the practical considerations of limited repair shop capacity and prioritized shop dispatching rules combine to make repair times not independent of one another. In this research a simulation model of a limited capacity repair facility with prioritized scheduling is used to explore a variety of heuristic approaches to the spares stocking decision. The heuristics are also compared with use of a model requiring independent repair times (even though that assumption is not valid here). The results show that even when repair time dependencies are present, the performance of a model which assumes independent repair times is quite good.