Minimum cost component test plans for evaluating reliability of a highly reliable parallel system

One approach to evaluating system reliability is the use of system based component test plans. Such plans have numerous advantages over complete system level tests, primarily in terms of time and cost savings. This paper considers one of the two basic building blocks of many complex systems, namely a system of n parallel components, and develops minimum cost component test plans for evaluating the reliability of such a system when the component reliabilities are known to be high. Two different decision rules are considered and the corresponding optimization problems are formulated and solved using techniques from mathematical programming. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44 : 401–418, 1997     

A recursive algorithm for a summed multinomial density function

An algorithm for calculating the probabilities of a summed multinomial density function which is recursive with n (the number of trials) is presented. Having application in inspector error models for auditing and quality control problems with Cartesian product structures, the algorithm is discussed in the context of computing optimal economic sampling plans. Computational experience with the algorithm is presented.     

Two‐stage component test plans for testing the reliability of a series system

A system reliability is often evaluated by individual tests of components that constitute the system. These component test plans have advantages over complete system based tests in terms of time and cost. In this paper, we consider the series system with n components, where the lifetime of the i‐th component follows exponential distribution with parameter λ_i. Assuming test costs for the components are different, we develop an efficient algorithm to design a two‐stage component test plan that satisfies the usual probability requirements on the system reliability and in addition minimizes the maximum expected cost. For the case of prior information in the form of upper bounds on λ_i's, we use the genetic algorithm to solve the associated optimization problems which are otherwise difficult to solve using mathematical programming techniques. The two‐stage component test plans are cost effective compared to single‐stage plans developed by Rajgopal and Mazumdar. We demonstrate through several numerical examples that our approach has the potential to reduce the overall testing costs significantly. © 2002 John Wiley & Sons, Inc. Naval Research Logistics, 49: 95–116, 2002; DOI 10.1002/nav.1051     

Optimal nonmyopic gambling strategy for the generalized Kelly criterion

We consider the optimal wagers to be made by a gambler who starts with a given initial wealth. The gambler faces a sequence of two-outcome games, i.e., “win” vs. “lose,” and wishes to maximize the expected value of his terminal utility. It has been shown by Kelly, Bellman, and others that if the terminal utility is of the form log x, where x is the terminal wealth, then the optimal policy is myopic, i.e., the optimal wager is always to bet a constant fraction of the wealth provided that the probability of winning exceeds the probability of losing. In this paper we provide a critique of the simple logarithmic assumption for the utility of terminal wealth and solve the problem with a more general utility function. We show that in the general case, the optimal policy is not myopic, and we provide analytic expressions for optimal wager decisions in terms of the problem parameters. We also provide conditions under which the optimal policy reduces to the simple myopic case. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44: 639–654, 1997     

Application of renewal theory to continuous sampling plans

Renewal theory is used to study the effectiveness of a class of continuous sampling plans first introduced by Dodge. This approach provides a simple way of viewing and computing the long-run Average Outgoing Quality (AOQ) and its maximum AOQL. More importantly, it is used to study the average outgoing quality in a short production run through an approximation formula AOQ^*(t). Formulas for AOQ and AOQ^*(t) are provided. By simulation, it is found that AOQ^*(t) is sufficiently accurate in situations corresponding to actual practice.     

Optimality of the greedy shooting strategy in the presence of incomplete damage information

Consider a situation where a single shooter engages, sequentially, a cluster of targets that may vary in terms of vulnerability and value or worth. Following the shooting of a round of fire at a certain target, the latter may either be killed or remain alive. We assume neither partial nor cumulative damage. If the target is killed, there is a possibility that the shooter is not aware of that fact and may keep on engaging that target. If the shooter recognizes a killed target as such, then this target is considered to be evidently killed. If the objective is to maximize the weighted expected number of killed targets, where the weight reflects the value of a target, then it is shown that a certain type of a shooting strategy, called a Greedy Strategy, is optimal under the general assumption that the more a target is engaged, but still not evidently killed, the less is the probability that the next round will be effective. If all weights are equal, then the greedy shooting strategy calls to engage, at each round, the least previously engaged target that is not evidently killed. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44: 613–622, 1997     

An approximate dynamic programing approach to the development of heuristics for the scheduling of impatient jobs in a clearing system

A single server is faced with a collection of jobs of varying duration and urgency. Each job has a random lifetime during which it is available for nonpreemptive service. Should a job's lifetime expire before its service begins then it is lost from the system unserved. The goal is to schedule the jobs for service to maximize the expected number served to completion. Two heuristics have been proposed in the literature. One (labeled π^S) operates a static priority among the job classes and works well in a “no premature job loss” limit, whereas the second (π^M) is a myopic heuristic which works well when lifetimes are short. Both can exhibit poor performance for problems at some distance from the regimes for which they were designed. We develop a robustly good heuristic by an approximative approach to the application of a policy improvement step to the asymptotically optimal heuristic π^S, in which we use a fluid model to obtain an approximation for the value function of π^S. The performance of the proposed heuristic is investigated in an extensive numerical study. © 2010 Wiley Periodicals, Inc. Naval Research Logistics 2010     

Selling to strategic and loss‐averse consumers: Stocking,procurement, and product design policies

Motivated by the presence of loss‐averse decision making behavior in practice, this article considers a supply chain consisting of a firm and strategic consumers who possess an S‐shaped loss‐averse utility function. In the model, consumers decide the purchase timing and the firm chooses the inventory level. We find that the loss‐averse consumers' strategic purchasing behavior is determined by their perceived gain and loss from strategic purchase delay, and the given rationing risk. Thus, the firm that is cognizant of this property tailors its inventory stocking policy based on the consumers' loss‐averse behavior such as their perceived values of gain and loss, and their sensitivity to them. We also demonstrate that the firm's equilibrium inventory stocking policy reflects both the economic logic of the traditional newsvendor inventory model, and the loss‐averse behavior of consumers. The equilibrium order quantity is significantly different from those derived from models that assume that the consumers are risk neutral and homogeneous in their valuations. We show that the firm that ignores strategic consumer's loss‐aversion behavior tends to keep an unnecessarily high inventory level that leads to excessive leftovers. Our numerical experiments further reveal that in some extreme cases the firm that ignores strategic consumer's loss‐aversion behavior generates almost 92% more leftovers than the firm that possesses consumers’ loss‐aversion information and takes it into account when making managerial decisions. To mitigate the consumer's forward‐looking behavior, we propose the adoption of the practice of agile supply chain management, which possesses the following attributes: (i) procuring inventory after observing real‐time demand information, (ii) enhanced design (which maintains the current production mix but improves the product performance to a higher level), and (iii) customized design (which maintains the current performance level but increases the variety of the current production line to meet consumers’ specific demands). We show that such a practice can induce the consumer to make early purchases by increasing their rationing risk, increasing the product value, or diversifying the product line. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 435–453, 2015     

Steady-state analysis of load balancing with Coxian-2 distributed service times

This paper studies load balancing for many-server (N servers) systems. Each server has a buffer of size b ? 1, and can have at most one job in service and b ? 1 jobs in the buffer. The service time of a job follows the Coxian-2 distribution. We focus on steady-state performance of load balancing policies in the heavy traffic regime such that the normalized load of system is λ = 1 ? N^?α for 0 < α < 0.5. We identify a set of policies that achieve asymptotic zero waiting. The set of policies include several classical policies such as join-the-shortest-queue (JSQ), join-the-idle-queue (JIQ), idle-one-first (I1F) and power-of-d-choices (Po d) with d = O(N^α log N). The proof of the main result is based on Stein's method and state space collapse. A key technical contribution of this paper is the iterative state space collapse approach that leads to a simple generator approximation when applying Stein's method.     

Bayesian estimation and optimal designs in partially accelerated life testing

A method of life testing is proposed which combines both ordinary and accelerated life-testing procedures. It is assumed that an item can be tested either in a standard environment or under stress. The amount of stress is fixed in advance and is the same for all items to be tested However, the time x at which an item on lest is taken out of the standard environment and put under stress can be chosen by the experimenter subject to a given cost structure. When an item is put under stress its lifetime is changed by the factor α. Let the random variable T denote the lifetime of an item in the standard environment, and let γ denote its lifetime under the partially accelerated test procedure just described. Then Y = T if T ≦ x, and Y = x + α (T > x) if T > x. It is assumed that T has an exponential distribution with parameter θ. The estimation of θ and α and the optimal design of a partially accelerated life test are studied in the framework of Bayesian decision theory.     

小子样条件下基于Normal-Poisson过程的性能可靠性评定

对于高可靠、长寿命产品,基于性能退化数据分析可靠性是一种行之有效的技术途径。结合航空航天产品性能退化的机理与现场试验小子样的特点,建立了基于Normal-Poisson过程的性能退化模型。论文在对产品性能退化建模的基础上,结合Bayes方法给出了退化模型参数的估计算法和可靠性推断的公式,最后结合实例说明了方法的有效性。     

某型滑翔增程靶弹方案弹道设计

针对某滑翔增程靶弹的无动力特性,综合各方面因素,提出一种具有近似平飞段的方案弹道。选择相关参数,设计了一种具有近似平飞段的高度变化律,提出了改进的攻角表达式,得到无动力靶弹三自由度铅垂平面的运动模型。数字仿真证明,这种方法合理可行,满足了靶弹各项战技指标,实现靶弹的近似平飞,方案弹道能较好地追踪给定高度变化,具有较高的工程应用价值。     

Acceptance sampling,imperfect production,and the optimality of zero defects

Acceptance sampling is often used to monitor the quality of raw materials and components when product testing is destructive, time-consuming, or expensive. In this paper we consider the effect of a buyer-imposed acceptance sampling policy on the optimal batch size and optimal quality level delivered by an expected cost minimizing supplier. We define quality as the supplier's process capability, i.e., the probability that a unit conforms to all product specifications, and we assume that unit cost is an increasing function of the quality level. We also assume that the supplier faces a known and constant “pass-through” cost, i.e., a fixed cost per defective unit passed on to the buyer. We show that the acceptance sampling plan has a significant impact on the supplier's optimal quality level, and we derive the conditions under which zero defects (100% conformance) is the policy that minimizes the supplier's expected annual cost. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44: 515–530, 1997     

One- and two-sided sampling plans based on the exponential distribution

In this paper we examine the one- and two-sided sampling plans for the exponential distribution. Solutions are provided for several situations arising out of the assumptions on the knowledge of the parameters of the distribution. The values of the constants are tabled in the special case of p₁ = p₂ for the two-sided plans.     

Some experiences using MIL-STD-105 in the united states air force

The historical and, to some extent, the current role of attribute inspection sampling in the United States Air Force is described. Some insight into consideration culminating in revisions made to the original MIL-STD-105 sampling plans is provided. These revisions were motivated from a practitioner's perspective rather than that of a statistical expert. Some significant administrative applications within the Air Force are described, and a practical method, based on the total amount of inspection, is given for distinguishing between sampling plans that have a fixed risk level (i.e., common value on the OC curves).     

基于D-S证据理论的炮兵战场目标价值分析*

针对如何依据目标情报资料和作战任务需要合理评估战场目标的价值,选择需要射击的目标和确定优先顺序,建立了战场目标价值评价体系,提出了一种运用D-S证据推理理论对炮兵战场目标价值进行分析的新途径,该方法运用D-S证据组合公式对目标繁杂、不确定信息的融合,能够很好地消除目标信息的不确定性,从而将具有主观不确定性信息的目标价值分析问题转化为普通的确定性决策问题。通过实例证明了方法的有效性。     

The effect of training data set size and the complexity of the separation function on neural network classification capability: The two-group case

Classification among groups is a crucial problem in managerial decision making. Classification techniques are used in: identifying stressed firms, classifying among consumer types, and rating of firms' bonds, etc. Neural networks are recognized as important and emerging methodologies in the area of classification. In this paper, we study the effect of training sample size and the neural network topology on the classification capability of neural networks. We also compare neural network capabilities with those of commonly used statistical methodologies. Experiments were designed and carried out on two-group classification problems to find answers to these questions. The prediction capability of the neural network models are better than traditional statistical models. The learning capability of the neural networks is improving compared to traditional models because the discriminate function is more complex. For real world classification problems, the usage of neural networks is highly recommended, for two reasons: learning capability and flexibility. Learning capability: Neural network classifies better in sterile experiments as performed in this research. Flexibility: Real life data are rarely not contaminated with noise, such as unknown distributions, and missing variables, etc. Neural networks differ from a statistical model that it is not dependent on any assumption concerning the data set distribution. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44: 699–717, 1997     

Computational aspects in multistage bayesian acceptance sampling

Simple criteria are found for reducing the computational effort in multistage Bayesian acceptance sampling. Regions of optimality are given for both terminal actions accept and reject. Also, criteria are presented for detecting nonoptimality of sets of sample sizes. Finally, nearly optimal (z,c^?,c⁺)-sampling plans are constructed by restricting attention to a small subset of sample sizes.     

基于效用函数的打击目标选择方法

针对打击目标选择问题,提出了一种基于效用函数的打击目标选择方法,根据效用函数理论和方法,对单个打击目标的价值进行了量化,对多元目标价值函数进行了构造,通过实例分析,说明该方法的有效性和合理性,从而为解决打击目标价值度量问题提供了一种新途径。     

Exact analysis of (R,s, S) inventory control systems with lost sales and zero lead time

We study an (R, s, S) inventory control policy with stochastic demand, lost sales, zero lead‐time and a target service level to be satisfied. The system is modeled as a discrete time Markov chain for which we present a novel approach to derive exact closed‐form solutions for the limiting distribution of the on‐hand inventory level at the end of a review period, given the reorder level (s) and order‐up‐to level (S). We then establish a relationship between the limiting distributions for adjacent values of the reorder point that is used in an efficient recursive algorithm to determine the optimal parameter values of the (R, s, S) replenishment policy. The algorithm is easy to implement and entails less effort than solving the steady‐state equations for the corresponding Markov model. Point‐of‐use hospital inventory systems share the essential characteristics of the inventory system we model, and a case study using real data from such a system shows that with our approach, optimal policies with significant savings in inventory management effort are easily obtained for a large family of items.