Repairable consecutive‐k‐out‐of‐n: F system with Markov dependence

In this article, a model for a repairable consecutive‐k‐out‐of‐n: F system with Markov dependence is studied. A binary vector is used to represent the system state. The failure rate of a component in the system depends on the state of the preceding component. The failure risk of a system state is then introduced. On the basis of the failure risk, a priority repair rule is adopted. Then the transition density matrix can be determined, and the analysis of the system reliability can be conducted accordingly. One example each of a linear and a circular system is then studied in detail to explain the model and methodology developed in this paper. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 18–39, 2000     

Linear compound algorithms for the partitioning problem

For a given set S of nonnegative integers the partitioning problem asks for a partition of S into two disjoint subsets S₁ and S₂ such that the sum of elements in S₁ is equal to the sum of elements in S₂. If additionally two elements (the kernels) r₁, r₂ ∈ S are given which must not be assigned to the same set S_i, we get the partitioning problem with kernels. For these NP‐complete problems the authors present two compound algorithms which consist both of three linear greedylike algorithms running independently. It is shown that the worst‐case performance of the heuristic for the ordinary partitioning problem is 12/11, while the second procedure for partitioning with kernels has a bound of 8/7. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 593–601, 2000     

Multivariate meta analysis with potentially correlated marketing study results

A univariate meta analysis is often used to summarize various study results on the same research hypothesis concerning an effect of interest. When several marketing studies produce sets of more than one effect, multivariate meta analysis can be conducted. Problems one might have with such a multivariate meta analysis are: (1) Several effects estimated in one model could be correlated to each other but their correlation is seldom published and (2) an estimated effect in one model could be correlated to the corresponding effect in the other model due to similar model specification or the data set partly shared, but their correlation is not known. Situations like (2) happen often in military recruiting studies. We employ a Monte‐Carlo simulation to evaluate how neglecting such potential correlation affects the result of a multivariate meta analysis in terms of Type I, Type II errors, and MSE. Simulation results indicate that such effect is not significant. What matters is rather the size of the variance component due to random error in multivariate effects. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 500–510, 2000.     

Estimating distribution functions from partially observed samples

Suppose that some components are initially operated in a certain condition and then switched to operating in a different condition. Working hours of the components in condition 1 and condition 2 are respectively observed. Of interest is the lifetime distribution F of the component in the second condition only, i.e., the distribution without the prior exposure to the first condition. In this paper, we propose a method to transform the lifetime obtained in condition 1 to an equivalent lifetime in condition 2 and then use the transformed data to estimate F. Both parametric and nonparametric approaches each with complete and censored data are discussed. Numerical studies are presented to investigate the performance of the method. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 521–530, 2000     

Selecting review periods for a coordinated multi‐item inventory model with staggered deliveries

Consider an N‐item, periodic review, infinite‐horizon, undiscounted, inventory model with stochastic demands, proportional holding and shortage costs, and full backlogging. For 1 ≤ j ≤ N, orders for item j can arrive in every period, and the cost of receiving them is negligible (as in a JIT setting). Every T_j periods, one reviews the current stock level of item j and decides on deliveries for each of the next T_j periods, thus incurring an item‐by‐item fixed cost k_j. There is also a joint fixed cost whenever any item is reviewed. The problem is to find review periods T₁, T₂, …, T_N and an ordering policy satisfying the average cost criterion. The current article builds on earlier results for the single‐item case. We prove an optimal policy exists, give conditions where it has a simple form, and develop a branch and bound algorithm for its computation. We also provide two heuristic policies with O(N) computational requirements. Computational experiments indicate that the branch and bound algorithm can handle normal demand problems with N ≤ 10 and that both heuristics do well for a wide variety of problems with N ranging from 2 to 200; moreover, the performance of our heuristics seems insensitive to N. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48:430–449, 2001     

Sequential and systematic sampling plans for the Markov‐dependent production process

Acceptance sampling plans are used to assess the quality of an ongoing production process, in addition to the lot acceptance. In this paper, we consider sampling inspection plans for monitoring the Markov‐dependent production process. We construct sequential plans that satisfy the usual probability requirements at acceptable quality level and rejectable quality level and, in addition, possess the minimum average sample number under semicurtailed inspection. As these plans result in large sample sizes, especially when the serial correlation is high, we suggest new plans called “systematic sampling plans.” The minimum average sample number systematic plans that satisfy the probability requirements are constructed. Our algorithm uses some simple recurrence relations to compute the required acceptance probabilities. The optimal systematic plans require much smaller sample sizes and acceptance numbers, compared to the sequential plans. However, they need larger production runs to make a decision. Tables for choosing appropriate sequential and systematic plans are provided. The problem of selecting the best systematic sampling plan is also addressed. The operating characteristic curves of some of the sequential and the systematic plans are compared, and are observed to be almost identical. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 451–467, 2001     

Reliability of a 2‐dimensional k‐within‐consecutive‐r × s‐out‐of‐m × n:F system

A 2‐dimensional rectangular (cylindrical) k‐within‐consecutive‐r × s‐out‐of‐m × n:F system is the rectangular (cylindrical) m × n‐system if the system fails whenever k components in a r × s‐submatrix fail. This paper proposes a recursive algorithm for the reliability of the 2‐dimensional k‐within‐consecutive‐r × s‐out‐m × n:F system, in the rectangular case and the cylindrical case. This algorithm requires min ( O (mk^r(n?s)), O (nk^s(m?r))), and O (mk^rn) computing time in the rectangular case and the cylindrical case, respectively. The proposed algorithm will be demonstrated and some numerical examples will be shown. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 625–637, 2001.     

On optimal aiming to hit a linear target

Typically weapon systems have an inherent systematic error and a random error for each round, centered around its mean point of impact. The systematic error is common to all aimings. Assume such a system for which there is a preassigned amount of ammunition of n rounds to engage a given target simultaneously, and which is capable of administering their fire with individual aiming points (allowing “offsets”). The objective is to determine the best aiming points for the system so as to maximize the probability of hitting the target by at least one of the n rounds. In this paper we focus on the special case where the target is linear (one‐dimensional) and there are no random errors. We prove that as long as the aiming error is symmetrically distributed and possesses one mode at zero, the optimal aiming is independent of the particular error distribution, and we specify the optimal aiming points. Possible extensions are further discussed, as well as civilian applications in manufacturing, radio‐electronics, and detection. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 323–333, 1999     

A heuristic for the two‐machine no‐wait openshop scheduling problem

In this paper the problem of minimizing makespan in a two‐machine openshop is examined. A heuristic algorithm is proposed, and its worst case performance ratio and complexity are analyzed. The average case performance is evaluated using an empirical study. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 129–145, 1999     

Simultaneous determination of production and maintenance schedules using in‐line equipment condition and yield information

In many manufacturing environments, equipment condition has a significant impact on product quality, or yield. This paper presents a semi‐Markov decision process model of a single‐stage production system with multiple products and multiple maintenance actions. The model simultaneously determines maintenance and production schedules, accounting for the fact that equipment condition affects the yield of each product differently. It extends earlier work by allowing the expected time between decision epochs to vary by both action and machine state, by allowing multiple maintenance actions, and by treating the outcome of maintenance as less than certain. Sufficient conditions are developed that ensure the monotonicity of both the optimal production and maintenance actions. While the maintenance conditions closely resemble previously studied conditions for this type of problem, the production conditions represent a significant departure from earlier results. The simultaneous solution method is compared to an approach commonly used in industry, where the maintenance and production problems are treated independently. Solving more than one thousand test problems confirms that the combination of both features of the model—accounting for product differences and solving the problems simultaneously—has a significant impact on performance. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2008