The optimal burn-in testing of repairable equipment

The subject of this paper is the utilization of the “infant mortality” or decreasing failure rate effect to improve the reliability of repairable devices. Decreasing failure rate implies the possibility that devices which exhibit it can be improved by “burn-in testing” of each unit. Such a test serves to accumulate operating time while shielded from the full costs and consequences of failure. A general formulation of the burn-in test decision for repairable devices is presented and some special cases are solved. A class of models, indexed by the degree of partial replacement present in the repair process, is considered and numerical results for the optimal policy are given for several members of that class. A comparison of those results reveals the profitability of testing increases with the complexity of the repairable device.     

Probabilistic models of decreasing failure rate processes

The “infant mortality” effect observed in the statistical treatment of reliability consists of a decreasing with age of the conditional probability of equipment failure (failure rate). One widely applicable explanatory hypothesis is that of population heterogeneity. This is developed here as a basis for several specific models of decreasing failure rate processes. Since, in the case of repairable devices, decreasing failure rate is often observed after the occurrence of failure and repair, consideration is extended to include repair in an explicit way. This union of failure and repair models is a fruitful one in view of the interaction between the two processes and gives a complete picture of the life of the device in terms of a stochastic process, usually with non-independent interfailure times. Four models, of particular significance due to their plausibility, mathematical tractability, and frugality of parameterization, are presented.     

The fixed charge problem

A fundamental unsolved problem in the programming area is one in which various activities have fixed charges (e.g., set-up time charges) if operating at a positive level. Properties of a general solution to this type problem are discussed in this paper. Under special circumstances it is shown that a fixed charge problem can be reduced to an ordinary linear programming problem.     

Integer points on the Gomory fractional cut (hyperplane)

In this paper we show that the Gomory fractional cut (hyperplane) for the integer program is either void of integer points or contains an infinite number of them. The conditions for each case are presented. Also, we derive a stronger cut from the hyperplane which does not intersect integer points.     

Air Power in the Six-Day War

In the aftermath of Israel's stunning victory over Egyptian, Jordanian and Syrian forces during the 1967 Six-Day War, accolades for the victory were often showered upon the Israeli Air Force (IAF). Indeed, many believed that it had been Israeli air power that had been the decisive element in the war by first eliminating the Arab air forces and then obliterating the Arab armies in turn. While the IAF did play an extremely important role in the fighting, it was not the decisive element of Israeli victory, and its impact was felt in very different ways from the common perception. Indeed, an appreciation of the true role of Israeli air power in the war reinforces both the importance of psychological factors in combat, and the ability of air forces to have a psychological impact disproportionate to their physical impact.     

Simplified estimates of the parameters of the double exponential distribution based on optimum order statistics from a middle-censored sample

In an ordered sample from a given population, a few of the consecutive observations from somewhere in the middle may be missing Further, we may be constrained to use a few, and not all, of the remaining observations for purposes of estimation of population parameters. In this paper, such a situation is considered for the double exponential distribution and best linear unbiased estimates are obtained for its parameters, based on a choice of an optimum set of order statistics when the number of observations in the set are prefixed.     

The search for an intelligent evader: Strategies for searcher and evader in the two-region problem

This paper considers the search for an evader concealed in one of two regions, each of which is characterized by its detection probability. The single-sided problem, in which the searcher is told the probability of the evader being located in a particular region, has been examined previously. We shall be concerned with the double-sided problem in which the evader chooses this probability secretly, although he may not subsequently move: his optimal strategy consists of that probability distribution which maximizes the expected time to detection, while the searcher's optimal strategy is the sequence of searches which limits the evader to this expected time. It transpires for this problem that optimal strategies for both searcher and evader may generally be obtained to a surprisingly good degree of approximation by using the optimal strategies for the closely related (but far more easily solved) problem in which the evader is completely free to move between searches.     

Postoptimality analysis in zero-one programming by implicit enumeration

The procedures for postoptimality analysis that are so much a part of linear programming studies have no simple counterparts in an integer programming context. In the case of Balas' Additive Algorithm, however, it would appear that the capacity of the technique to facilitate certain types of postoptimality analysis has not been fully exploited. This paper proposes an extension of the additive algorithm that utilizes insights generated while solving the original problem to do subsequent analysis upon it. In particular, procedures are developed for doing limited parameter ranging and for seeking new optima in light of parameter changes.