A note on the stochastic shortest-route problem

This paper develops an algorithm for a “shortest route” network problem in which it is desired to find the path which yields the shortest expected distance through the network. It is assumed that if a particular arc is chosen, then there is a finite probability that an adjacent arc will be traversed instead. Backward induction is used and appropriate recursion formulae are developed. A numerical example is provided.     

Explicit modeling of detection within a stochastic duel

Many mathematical models have been formulated to describe combat between two weapon systems. However, until recently duel models did not explicitly represent target detection within a duel, leading to the necessity for the development of new model for each tactical situation. An earlier article by two of the authors described a duel between weapons with constant firing times and explicit modeling of detection. This article enhances the study of this form of duel between weapons by introducing a variable parameter for firing times. This enhancement removes the discontinuities evident during parametric analysis of the earlier model and hence provides a more coherent model of this combat situation. © 1993 John Wiley & Sons, Inc.     

Reliability growth of repairable systems

This paper considers the problem of modeling the reliability of a repairable system or device that is experiencing reliability improvement. Such a situation arises when system failure modes are gradually being corrected by a test-fix-test-fix procedure, which may include design changes. A dynamic reliability model for this process is discussed and statistical techniques are derived for estimating the model parameters and for testing the goodness-of-fit to observed data. The reliability model analyzed was first proposed as a graphical technique known as Duane plots, but can also be viewed as a nonhomogeneous Poisson process with a particular mean value function.     

Shifting power,preventive logic,and the response of the target: Germany,Russia, and the First World War

If a declining state has incentives for preventive war, the rising state should have incentives to delay a confrontation until it is stronger. We develop the theoretical paradox and examine the July 1914 crisis. Why did Russia, rising relative to Germany, not adopt a buying-time strategy? We argue that although most Russian leaders hoped to avoid a confrontation, they feared that the failure to support Serbia would lead to a loss of Russian credibility and a significant setback to Russia’s position in the Balkans, one that could not easily be reversed, even with Russia’s expected increase in relative military power.     

Variables inspection for SPC‐quarantined production

When a control chart signals an out‐of‐control condition for a production process, it may be desirable to “quarantine” all units produced since the last in‐control SPC sample. This paper presents an efficient procedure for variables inspection of such “SPC quarantined” product. A Bayesian sequential inspection procedure is developed which determines whether the out of control production is of acceptable quality. By inspecting the units in reverse of the order in which they were produced, the procedure is also capable of detecting the point at which the process went out of control, thus eliminating the need to inspect units produced prior to the onset of the out of control condition. Numerical examples are presented, and the performance characteristics of the procedure are demonstrated using Monte Carlo simulation. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 159–171, 2001     

Combat modeling of remotely targeted vehicles and a battery against a moving target

This paper considers a combined system composed of multiple stand-by remotely piloted vehicles (RPVs) and a single battery against a single passive enemy target, where the target, if not killed, is allowed to change its location after each attack. The RPV has the duty to report on target acquisition, to confirm a target kill, and to pass information on any change in target location after each battery attack. The battery has the duty to attack the target on the basis of the target location information provided to it by the RPV. We develop a closed-form expression for the time-dependent state probabilities of the system, which can be used to compute several important combat measures of effectiveness, including (a) the time-varying mean and variance of the number of the RPVs being alive and of the surviving enemy target, (b) the mission success, mission failure, and combat draw probabilities, and (c) the mean and variance of the combat duration time. Illustrative numerical examples are solved for these combat measures, and sensitivity analyses are performed with respect to target acquisition time and target kill probability. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 645–667, 1998     

Scheduling stochastic jobs with asymmetric earliness and tardiness penalties

We consider a stochastic counterpart of the well-known earliness-tardiness scheduling problem with a common due date, in which n stochastic jobs are to be processed on a single machine. The processing times of the jobs are independent and normally distributed random variables with known means and known variances that are proportional to the means. The due dates of the jobs are random variables following a common probability distribution. The objective is to minimize the expectation of a weighted combination of the earliness penalty, the tardiness penalty, and the flow-time penalty. One of our main results is that an optimal sequence for the problem must be V-shaped with respect to the mean processing times. Other characterizations of the optimal solution are also established. Two algorithms are proposed, which can generate optimal or near-optimal solutions in pseudopolynomial time. The proposed algorithms are also extended to problems where processing times do not satisfy the assumption in the model above, and are evaluated when processing times follow different probability distributions, including general normal (without the proportional relation between variances and means), uniform, Laplace, and exponential. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44, 531–557, 1997.