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.     

Estimating a survival curve when new is better than used with respect to a distinguished set

Hollander, Park, and Proschan define a survival function S of a positive random variable X to be new better than used at age t₀ (NBU-{t₀}) if S satisfies $ \begin{array}{*{20}c} {\frac{{S(x + t_0)}}{{S\left({t_0} \right)}} \le S\left(x \right),} & {{\rm for}\,{\rm all}\,x\, \ge \,0,} \\ \end{array}$ where S(x) = P(X > x). The NBU-{t₀} class is a special case of the NBU-A family of survival distributions, where A is a subset of [0, ∞). These families introduce a variety of modeling possibilities for use in reliability studies. We treat problems of nonparametric estimation of survival functions from these classes by estimators which are themselves members of the classes of interest. For a number of such classes, a recursive estimation technique is shown to produce closed-form estimators which are strongly consistent and converge to the true survival distribution at optimal rates. For other classes, additional assumptions are required to guarantee the consistency of recursive estimators. As an example of the latter case, we demonstrate the consistency of a recursive estimator for S ∈ NBU-[t₀, ∞) based on lifetime data from items surviving a preliminary “burn-in” test. The relative precision of the empirical survival curve and several recursive estimators of S are investigated via simulation; the results provide support for the claim that recursive estimators are superior to the empirical survival curve in restricted nonparametric estimation problems of the type studied here.     

Optimal replacement policies for multistate deteriorating systems

We consider state-age-dependent replacement policies for a multistate deteriorating system. We assume that operating cost rates and replacement costs are both functions of the underlying states. Replacement times and sojourn times in different states are all state-dependent random variables. The optimization criterion is to minimize the expected long-run cost rate. A policy-improvement algorithm to derive the optimal policy is presented. We show that under reasonable assumptions, the optimal replacement policies have monotonic properties. In particular, when the failure-rate functions are nonincreasing, or when all the replacement costs and the expected replacement times are independent of state, we show that the optimal policies are only state dependent. Examples are given to illustrate the structure of the optimal policies in the special case when the sojourntime distributions are Weibull. © 1994 John Wiley & Sons, Inc.     

Optimal inspection under semi-markovian deterioration: Basic results

This article develops a model for determining the optimal inspection schedule for a system which deteriorates according to a semi-Markov process that progresses through three states: good, defective, and bad. A binary test is used, and false positives may occur. A true positive results in an action that reduces the likelihood of entering the bad state, but at most one such corrective action can occur during the lifetime of the system. Costs are associated with each inspection, each false positive, the corrective action, and the entrance into the bad state. Dynamic programming is used to compute the minimum expected cost, which is a function of the age of the system. The optimal inspection schedule is readily derived from this value function. Computational examples are provided. This model is appropriate for medical screening or for a mission where there is only one spare part.     

The Imperfect Peace: Explaining Paramilitary Violence in Northern Ireland

This article examines why paramilitary campaigns in Northern Ireland have continued despite the current peace process. In advancing three instrumental explanations of paramilitary violence, the author provides a useful analytical framework which shows that while organizational interpretations are dominating the public discourse, republicans and loyalists continue to use paramilitary violence as a strategic means of threat and coercion. Furthermore, even though policy implications are not discussed in detail, it will be demonstrated that the dominance of organizational imperatives has resulted in excessive leniency by the state, which - in turn - has contributed to the fragility of the peace process.     

On the (S − 1, S) lost sales inventory model with priority demand classes

In this paper an inventory model with several demand classes, prioritised according to importance, is analysed. We consider a lot‐for‐lot or (S ? 1, S) inventory model with lost sales. For each demand class there is a critical stock level at and below which demand from that class is not satisfied from stock on hand. In this way stock is retained to meet demand from higher priority demand classes. A set of such critical levels determines the stocking policy. For Poisson demand and a generally distributed lead time, we derive expressions for the service levels for each demand class and the average total cost per unit time. Efficient solution methods for obtaining optimal policies, with and without service level constraints, are presented. Numerical experiments in which the solution methods are tested demonstrate that significant cost reductions can be achieved by distinguishing between demand classes. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 593–610, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10032     

Sensitivity curves for effective project management

A key problem in project management is to decide which activities are the most important to manage and how best to manage them. A considerable amount of literature has been devoted to assigning “importance” measures to activities to help with this important task. When activity times are modeled as random variables, these activity importance measures are more complex and difficult to use. A key problem with all existing measures is that they summarize the importance in a single number. The result is that it is difficult for managers to determine a range of times for an activity that might be acceptable or unacceptable. In this paper, we develop sensitivity curves that display the most useful measures of project performance (in terms of schedule) as a function of an activity's time. The structure of the networks allows us to efficiently estimate these curves for all desired activities, all desired time ranges, and all desired measures in a single set of simulation runs. The resulting curves provide insights that are not available when considering summarized measures alone. Chief among these insights is the ability to identify an acceptable range of times for an activity that will not lead to negative scheduling consequences. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 481–497, 2003     

Age replacement policies in two time scales

We develop and estimate optimal age replacement policies for devices whose age is measured in two time scales. For example, the age of a jet engine can be measured in the number of flight hours and the number of landings. Under a single‐scale age replacement policy, a device is replaced at age τ or upon failure, whichever occurs first. We show that a natural generalization to two scales is to replace nonfailed devices when their usage path crosses the boundary of a two‐dimensional region M, where M is a lower set with respect to the matrix partial order. For lifetimes measured in two scales, we consider devices that age along linear usage paths. We generalize the single‐scale long‐run average cost, estimate optimal two‐scale policies, and give an example. We note that these policies are strongly consistent estimators of the true optimal policies under mild conditions, and study small‐sample behavior using simulation. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 592–613, 2003.