Optimal sample size allocation for tests with multiple levels of stress with extreme value regression

In this article, we discuss the optimal allocation problem in a multiple stress levels life‐testing experiment when an extreme value regression model is used for statistical analysis. We derive the maximum likelihood estimators, the Fisher information, and the asymptotic variance–covariance matrix of the maximum likelihood estimators. Three optimality criteria are defined and the optimal allocation of units for two‐ and k‐stress level situations are determined. We demonstrate the efficiency of the optimal allocation of units in a multiple stress levels life‐testing experiment by using real experimental situations discussed earlier by McCool and Nelson and Meeker. Monte Carlo simulations are used to show that the optimality results hold for small sample sizes as well. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Constrained minimax optimization of continuous search efforts for the detection of a stationary target

Analytical resolution of search theory problems, as formalized by B.O. Koopman, may be applied with some model extension to various resource management issues. However, a fundamental prerequisite is the knowledge of the prior target density. Though this assumption has the definite advantage of simplicity, its drawback is clearly that target reactivity is not taken into account. As a preliminary step towards reactive target study stands the problem of resource planning under a min–max game context. This paper is related to Nakai's work about the game planning of resources for the detection of a stationary target. However, this initial problem is extended by adding new and more general constraints, allowing a more realistic modeling of the target and searcher behaviors. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Production to order and off‐line inspection when the production process is partially observable

This study combines inspection and lot‐sizing decisions. The issue is whether to INSPECT another unit or PRODUCE a new lot. A unit produced is either conforming or defective. Demand need to be satisfied in full, by conforming units only. The production process may switch from a “good” state to a “bad” state, at constant rate. The proportion of conforming units in the good state is higher than in the bad state. The true state is unobservable and can only be inferred from the quality of units inspected. We thus update, after each inspection, the probability that the unit, next candidate for inspection, was produced while the production process was in the good state. That “good‐state‐probability” is the basis for our decision to INSPECT or PRODUCE. We prove that the optimal policy has a simple form: INSPECT only if the good‐state‐probability exceeds a control limit. We provide a methodology to calculate the optimal lot size and the expected costs associated with INSPECT and PRODUCE. Surprisingly, we find that the control limit, as a function of the demand (and other problem parameters) is not necessarily monotone. Also, counter to intuition, it is possible that the optimal action is PRODUCE, after revealing a conforming unit. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Probabilistic resource pooling games

We study a setting with a single type of resource and with several players, each associated with a single resource (of this type). Unavailability of these resources comes unexpectedly and with player‐specific costs. Players can cooperate by reallocating the available resources to the ones that need the resources most and let those who suffer the least absorb all the costs. We address the cost savings allocation problem with concepts of cooperative game theory. In particular, we formulate a probabilistic resource pooling game and study them on various properties. We show that these games are not necessarily convex, do have non‐empty cores, and are totally balanced. The latter two are shown via an interesting relationship with Böhm‐Bawerk horse market games. Next, we present an intuitive class of allocation rules for which the resulting allocations are core members and study an allocation rule within this class of allocation rules with an appealing fairness property. Finally, we show that our results can be applied to a spare parts pooling situation.     

基于非线性Kalman滤波的导航系统误差补偿技术

针对非线性非高斯导航系统信息处理问题,采用自组织算法、神经网络和遗传算法等改进传统非线性Kalman滤波算法,构建一种自适应的组合导航系统。应用具有冗余趋势项的自组织算法、Volterra神经网络和遗传算法,建立导航系统误差的非线性预测模型,进而计算得到其预测值;将该预测值与Kalman滤波算法求得的估计值进行比较得到差值,以此监测Kalman滤波算法的工作状态;采用自适应控制方法,在导航系统结构层面改进Kalman滤波算法,构建新型的导航系统误差补偿模型。开展基于导航系统KIND-34的半实物仿真研究,应用所提出的改进方法改善了导航系统误差的补偿效果,提高了组合导航系统的自适应能力和容错能力。     

Layers of Experiments with Adaptive Combined Design

In the field of nanofabrication, engineers often face unique challenges in resource‐limited experimental budgets, the sensitive nature of process behavior with respect to controllable variables, and highly demanding tolerance requirements. To effectively overcome these challenges, this article proposes a methodology for a sequential design of experiments through batches of experimental runs, aptly named Layers of Experiments with Adaptive Combined Design (LoE/ACD). In higher layers, where process behavior is less understood, experimental regions cover more design space and data points are more spread out. In lower layers, experimental regions are more focused to improve understanding of process sensitivities in a local, data‐rich environment. The experimental design is a combination of a space‐filling and an optimal design with a tuning parameter that is dependent on the amount of information accumulated over the various layers. The proposed LoE/ACD method is applied to optimize a carbon dioxide (epet‐CO2) assisted deposition process for fabricating silver nanoparticles with pressure and temperature variables. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 127–142, 2015     

Single batch machine scheduling with deliveries

We consider the problem of scheduling a set of n jobs on a single batch machine, where several jobs can be processed simultaneously. Each job j has a processing time p_j and a size s_j. All jobs are available for processing at time 0. The batch machine has a capacity D. Several jobs can be batched together and processed simultaneously, provided that the total size of the jobs in the batch does not exceed D. The processing time of a batch is the largest processing time among all jobs in the batch. There is a single vehicle available for delivery of the finished products to the customer, and the vehicle has capacity K. We assume that K = rD, where and r is an integer. The travel time of the vehicle is T; that is, T is the time from the manufacturer to the customer. Our goal is to find a schedule of the jobs and a delivery plan so that the service span is minimized, where the service span is the time that the last job is delivered to the customer. We show that if the jobs have identical sizes, then we can find a schedule and delivery plan in time such that the service span is minimum. If the jobs have identical processing times, then we can find a schedule and delivery plan in time such that the service span is asymptotically at most 11/9 times the optimal service span. When the jobs have arbitrary processing times and arbitrary sizes, then we can find a schedule and delivery plan in time such that the service span is asymptotically at most twice the optimal service span. We also derive upper bounds of the absolute worst‐case ratios in both cases. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 470–482, 2015     

Choosing arrival process models for service systems: Tests of a nonhomogeneous Poisson process

Service systems such as call centers and hospital emergency rooms typically have strongly time‐varying arrival rates. Thus, a nonhomogeneous Poisson process (NHPP) is a natural model for the arrival process in a queueing model for performance analysis. Nevertheless, it is important to perform statistical tests with service system data to confirm that an NHPP is actually appropriate, as emphasized by Brown et al. [8]. They suggested a specific statistical test based on the Kolmogorov–Smirnov (KS) statistic after exploiting the conditional‐uniform (CU) property to transform the NHPP into a sequence of i.i.d. random variables uniformly distributed on [0,1] and then performing a logarithmic transformation of the data. We investigate why it is important to perform the final data transformation and consider what form it should take. We conduct extensive simulation experiments to study the power of these alternative statistical tests. We conclude that the general approach of Brown et al. [8] is excellent, but that an alternative data transformation proposed by Lewis [22], drawing upon Durbin [10], produces a test of an NHPP test with consistently greater power. We also conclude that the KS test after the CU transformation, without any additional data transformation, tends to be best to test against alternative hypotheses that primarily differ from an NHPP only through stochastic and time dependence. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 66–90, 2014     

Some aging properties of parallel and series systems with a random number of components

In this article, we study aging properties of parallel and series systems with a random number of components. We show that the decreasing likelihood ratio property is closed under the formation of random minima. We also show, by counterexamples, that other aging properties are not closed under the formation of random minima or maxima. Some mistakes in the literature are corrected. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 238–243, 2014     

An interactive approach to multicriteria sorting for quasiconcave value functions

In this article, we develop an interactive algorithm to place alternatives in ordered preference classes for a decision maker (DM) with an increasing quasiconcave value function. Such value functions are quite general in that they include linear and concave value functions. Our aim is to elicit sorting information from the DM as few times as possible; our algorithm places other alternatives using previous responses from the DM utilizing properties of quasiconcave value functions. As an application, we sort 81 global MBA programs into preference classes using criteria such as alumni career progress, idea generation, and diversity. We study the performance of our proposed algorithm, when we change the number of criteria, number of alternatives, and introduce response errors. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 447–457, 2014