Statistical equivalency and optimality of simple step‐stress accelerated test plans for the exponential distribution

Accelerated life testing (ALT) is commonly used to obtain reliability information about a product in a timely manner. Several stress loading designs have been proposed and recent research interests have emerged concerning the development of equivalent ALT plans. Step‐stress ALT (SSALT) is one of the most commonly used stress loadings because it usually shortens the test duration and reduces the number of required test units. This article considers two fundamental questions when designing a SSALT and provides formal proofs in answer to each. Namely: (1) can a simple SSALT be designed so that it is equivalent to other stress loading designs? (2) when optimizing a multilevel SSALT, does it degenerate to a simple SSALT plan? The answers to both queries, under certain reasonable model assumptions, are shown to be a qualified YES. In addition, we provide an argument to support the rationale of a common practice in designing a SSALT, that is, setting the higher stress level as high as possible in a SSALT plan. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2013     

Outbound supply chain network design with mode selection and lead time considerations

We present a large‐scale network design model for the outbound supply chain of an automotive company that considers transportation mode selection (road vs. rail) and explicitly models the relationship between lead times and the volume of flow through the nodes of the network. We formulate the problem as a nonlinear zero‐one integer program, reformulate it to obtain a linear integer model, and develop a Lagrangian heuristic for its solution that gives near‐optimal results in reasonable time. We also present scenario analyses that examine the behavior of the supply chain under different parameter settings and the performance of the solution procedures under different experimental conditions. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

On optimal system designs in reliability‐economics frameworks

Reliability Economics is a field that can be defined as the collection of all problems in which there is tension between the performance of systems of interest and their cost. Given such a problem, the aim is to resolve the tension through an optimization process that identifies the system which maximizes some appropriate criterion function (e.g. expected lifetime per unit cost). In this paper, we focus on coherent systems of n independent and identically distributed (iid) components and mixtures thereof, and characterize both a system's performance and cost as functions of the system's signature vector (Samaniego, IEEE Trans Reliabil (1985) 69–72). For a given family of criterion functions, a variety of optimality results are obtained for systems of arbitrary order n. Approximations are developed and justified when the underlying component distribution is unknown. Assuming the availability of an auxiliary sample of N component failure times, the asymptotic theory of L‐estimators is adapted for the purpose of establishing the consistency and asymptotic normality of the proposed estimators of the expected ordered failure times of the n components of the systems under study. These results lead to the identification of ε‐optimal systems relative to the chosen criterion function. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Strategic obfuscation of production capacities

Recent supply‐chain models that study competition among capacity‐constrained producers omit the possibility of producers strategically setting wholesale prices to create uncertainty with regards to (i.e., to obfuscate) their production capacities. To shed some light on this possibility, we study strategic obfuscation in a supply‐chain model comprised of two competing producers and a retailer, where one of the producers faces a privately‐known capacity constraint. We show that capacity obfuscation can strictly increase the obfuscating producer's profit, therefore, presenting a clear incentive for such practices. Moreover, we identify conditions under which both producers' profits increase. In effect, obfuscation enables producers to tacitly collude and charge higher wholesale prices by moderating competition between producers. The retailer, in contrast, suffers a loss in profit, raises retail prices, while overall channel profits decrease. We show that the extent of capacity obfuscation is limited by its cost and by a strategic retailer's incentive to facilitate a deterrence. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 244–267, 2014     

Optimization of steerable sensor network for threat detection

A Markov chain approach to detecting a threat in a given surveillance zone by a network of steerable sensors is presented. The network has a finite number of predetermined states, and transition from one state to another follows a Markov chain. Under the assumption that the threat avoids detection, two game theoretic problems for finding an optimal Markov chain (two surveillance strategies) are formulated: the first maximizes the probability of threat detection for two consecutive detection periods, whereas the second minimizes the average time of detection for the worst‐case threat's trajectory. Both problems are reduced to linear programming, and special techniques are suggested to solve them. For a dynamic environment with moving noise sources, the optimal Markov chain changes at each detection period, and the rate of convergence of the Markov chain to its stationary distribution is analyzed. Both surveillance strategies are tested in numerical experiments and compared one with another. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

Lanchester attrition of interpenetrating forces

To approximate the solutions of detailed simulations of interpenetrating forces (or possibly to assist in curtailing Monte Carlo calculations), this article provides solutions to a simple problem assuming that the speed of advance is constant; the only interactions are local; Lanchester's linear or square law applies; force distributions are continuous if not initially uniform in depth. The resultant partial differential equations are solvable (1) in closed form if attrition is minimal or (2) with pain when attrition is sufficient to annihilate the leading edge of a force. This is exemplified only for the square law, where one must solve an integrodifferential equation for an ancillary function. A general solution is given for either law, and for the latter case a more complete one, assuming that initial force distributions are uniform. Useful properties of an unusual class of Bessel functions needed for this analysis are given in an appendix. Copies of computer programs are available.