Application of the stein-chen method for bounds and limit theorems in the reliability of coherent structures

The Stein-Chen method for establishing Poisson convergence is used to approximate the reliability of coherent systems with exponential-type distribution functions. These bounds lead to quite general limit theorems for the lifetime distribution of large coherent systems. © 1993 John Wiley & Sons, Inc.     

A search game with a protector

A classic problem in Search Theory is one in which a searcher allocates resources to the points of the integer interval [1, n] in an attempt to find an object which has been hidden in them using a known probability function. In this paper we consider a modification of this problem in which there is a protector who can also allocate resources to the points; allocating these resources makes it more difficult for the searcher to find an object. We model the situation as a two‐person non‐zero‐sum game so that we can take into account the fact that using resources can be costly. It is shown that this game has a unique Nash equilibrium when the searcher's probability of finding an object located at point i is of the form (1 − exp (−λ_ix_i)) exp (−μ_iy_i) when the searcher and protector allocate resources x_i and y_i respectively to point i. An algorithm to find this Nash equilibrium is given. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47:85–96, 2000     

Optimal maintenance and replacement policy for a deteriorating system with increased mean downtime

The problem of imperfect preventive maintenance (pm) and replacement schedule for a system which works below a specified failure rate is studied. For a given planning period, the optimal schedule for replacements to minimize the total cost is obtained. This article presents a branching algorithm with effective dominance rules to obtain the optimal schedule. Numerical illustration and computational experience are also presented.     

A generalized inspection game

The paper addresses the problem of a patrol trying to stop smugglers who are attempting to ship a cargo of perishable contraband across a strait in one of M time units. The situation was modeled as a two-person zero-sum game of exhaustion by Thomas and Nisgav and this article extends their results. The game has many characteristics in common with the Inspection Game in Owen's book on Game Theory; this Inspection Game is generalized and the relations between the two games are discussed.     

Continuous sampling plans for markov-dependent production processes

This article discusses the behavior of three continuous sampling plans: continuous sampling plan 1 (CSP 1) and continuous sampling plan 2 (CSP 2) developed by Dodge [5] and Dodge and Torrey [7], and multilevel continuous sampling plan 2 (MLP 2) developed by Lieberman and Solomon [11], when the quality of successive units in a continuous production process follows a two-state time-homogeneous Markov chain. We first derive the average outgoing quality (AOQ) expressions of these plans. Exact procedures for determining the average outgoing quality limit (AOQL) can be obtained only for CSP 1. For CSP 2 and MLP 2 plans, iterative procedures have been used to obtain the AOQL contours. For these plans, it is assumed that the serial correlation coefficient between the two consecutive random variables of the Markov chain is known. In addition, estimation procedures for the coefficient are given. We show that if the serial correlation coefficient of the Markov chain is positive (negative), the AOQL is increased (decreased) as compared to the case when the successive units in the production process follows a Bernoulli pattern. Let r denote the number of production units examined in succession which are found to be of good quality and k denote the inverse of the sampling fraction employed when quality is good. Then if r and k are sufficiently small, it is observed from the graph that, for small departures of the serial correlation coefficient from zero, the AOQL values do not differ significantly for each of the three plans; whereas for sufficiently large values of r and k, the AOQL values differ significantly. Various aspects of these plans, such as their operating characteristics 2 (OC 2) and the serial correlation coefficient, are discussed.     

A continuous game of ambush

The article considers a two-person competitive problem in which a traveller wishes to choose a path across a rectangle from left to right in such a way as to avoid being ambushed by his adversary who has placed obstacles within the rectangle. Our results supplement those that have already been obtained by Ruckle and they indicate that, under certain conditions, the players need to adopt rather sophisticated strategies if they are to act optimally. This suggests that a complete solution to the problem could be difficult.     

Inventory cost impact of order processing priorities based on demand uncertainty

We evaluate an approach to decrease inventory costs at retail inventory locations that share a production facility. The retail locations sell the same product but differ in the variance of retail demand. Inventory policies at retail locations generate replenishment orders for the production facility. The production facility carries no finished goods inventory. Thus, production lead time for an order is the sojourn time in a single server queueing system. This lead time affects inventory costs at retail locations. We examine the impact of moving from a First Come First Served (FCFS) production rule for orders arriving at the production facility to a rule in which we provide non‐preemptive priority (PR) to orders from retail locations with higher demand uncertainty. We provide three approximations for the ratio of inventory costs under PR and FCFS and use them to identify conditions under which PR decreases retail inventory costs over FCFS. We then use a Direct Approach to establish conditions when PR decreases retail inventory costs over FCFS. We extend the results to orders from locations that differ in the mean and variance of demand uncertainty. The analysis suggests that tailoring lead times to product demand characteristics may decrease system inventory costs. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 376–390, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10016     

The socialization of military power: security cooperation and doctrine development through multinational military exercises

Multinational Military Exercises (MMEs) are often viewed by states as opportunities to increase interoperability, improve cooperation, and solve common security problems. We argue that in addition to this, MMEs work as tools to shape the shared beliefs of coalition partners surrounding threat. Specifically, MMEs allow multinational forces to identify best practices, consolidate beliefs, and codify behavior through doctrine, typically by means of some institutional process. We examine our argument on MMEs through an analysis of various multinational and coalition partner efforts to identify security threats and cooperate through the development of common doctrine at the strategic, operational, and tactical levels of warfare. Our analysis suggests that the use of MMEs for doctrine development does help to socialize states in terms of identifying common threats and subsequently sharing a process by which to address them.     

Single-period inventory models with demand uncertainty and quantity discounts: Behavioral implications and a new solution procedure

Quantity discounts are considered in the context of the single-period inventory model known as “the newsboy problem.” It is argued that the behavioral implications of the all-units discount schedule are more complex and interesting than the literature has suggested. Consideration of this behavior and the use of marginal analysis lead to a new method for solving this problem that is both conceptually simpler and more efficient than the traditional approach. This marginal-cost solution procedure is described graphically, an algorithm is presented, and an example is used to demonstrate that this solution procedure can be extended easily to handle complex discount schedules, such as some combined (simultaneously applied) purchasing and transportation cost discount schedules.