Optimal maintenance models for systems subject to failure–A Review

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.     

Book reviews

Military Helicopters. By E. J. Everett‐Heath, G. M. Moss, A. W. Mowat and K. E. Reid. Brassey's, London (1990), ISBN 0–08–037341–0 (hardcover), ISBN 0–08–036716‐X (flexicover), £22.50 (hardcover), £12.95 (flexicover)

The Killing Ground: the British Army, the Western Front and the Emergence of Modern Warfare 1900–1918. By Tim Travers. Unwin‐Hyman, London (1990), ISBN 0–04–4457367, £11.95

The Influence of S. L. A. Marshall on the United States Army. By Major F. D. G. Williams. TRADOC Historical Monograph Series, Fort Monroe, VA (1990)     

Simulating stable stochastic systems,V: Comparison of ratio estimators

The regenerative method for estimating parameters in a simulation requires the simulator to estimate the ratio of two means. Five point estimates and four confidence intervals for this ratio have been computed for three stochastic simulations. The jackknife method appears to be the most promising for both point and interval estimation.     

Parametric studies in transportation-type problems

In this paper we present some results in parametric studies on several transportation-type problems. Specifically, a characterization is obtained for the optimal values of the variables in the problem of determining an optimal growth path in a logistics system. We also derive an upper bound beyond which the optimal growth path remains the same. The results are then extended to the goal programming model and the prespecified market growth rate problem.     

Order-preserving allocation of jobs to two machines

In this paper, we consider the problem of minimizing the mean flow time of jobs to be processed on two machines. The jobs have a predetermined order, perhaps reflecting the order of arrival, and each job has a known processing time. We wish to assign the jobs to machines so as to minimize the mean flow time, with the constraint that the original order must be preserved within the subset of jobs assigned to each machine. An efficient algorithm based on dynamic programming is developed.     

A queue with waiting time dependent service times

Sufficient conditions are developed for the ergodicity of a single server, first-come-first-serve queue with waiting time dependent service times.     

Queueing models for spares provisioning

A population of items which break down at random times and require repair is studied (the classic “machine repair problem with spares”). It is desired to determine the number of repair channels and spares required over a multiyear planning horizon in which population size and component reliability varies, and a service level constraint is imposed. When an item fails, a spare (if available) is immediately dispatched to replace the failed item. The failed item is removed, transported to the repair depot, repaired, and then placed in the spares pool (which is constrained to be empty not more than 10% of the time) unless there is a backlog of requests for spares, in which case it is dispatched immediately. The first model considered treats removal, transportation, and repair as one service operation. The second model is a series queue which allows for the separate treatment of removal, transportation, and repair. Breakdowns are assumed Poisson and repair times exponential.     

Optimum sequential search with discrete locations and random acceptance errors

Much work has been done in search theory; however, very little effort has occurred where an object's presence at a location can be accepted when no object is present there. The case analyzed is of this type. The number of locations is finite, a single object is stationary at one location, and only one location is observed each step of the search. The object's location has a known prior probability distribution. Also known are the conditional probability of acceptance given the object's absence (small) and the conditional probability of rejection given the object's presence (not too large); these Probabilities remain fixed for all searching and locations. The class of sequential search policies which terminate the search at the first acceptance is assumed. A single two-part optimization criterion is considered. The search sequence is found which (i) minimizes the probability of obtaining n rejections in the first n steps for all n, and (ii) maximizes the probability that the first acceptance occurs within the first n steps and occurs at the object's location for all n. The optimum sequential search policy specifies that the next location observed is one with the largest posterior probability of the object's presence (evaluated after each step from Bayes Rule) and that the object is at the first location where acceptance occurs. Placement at the first acceptance seems appropriate when the conditional probability of acceptance given the object's absence is sufficiently small. Search always terminates (with probability one). Optimum truncated sequential policies are also considered. Methods are given for evaluating some pertinent properties and for investigating the possibility that no object occurs at any location.