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     

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.     

Incremental approximation of optimal allocations

This paper concerns the approximation of optimal allocations by δ allocations. δ allocations are obtained by fixing an increment δ of effort and deciding at each step upon a single cell in which to allocate the entire increment. It is shown that δ allocations may be used as a simple method of approximating optimal allocations of effort resulting from constrained separable optimization problems involving a finite number of cells. The results are applied to find δ allocations (called δ plans) which approximate optimal search plans. δ plans have the property that as δ → 0, the mean time to find the target using a δ plan approaches the mean time when using the optimal plan. δ plans have the advantage that. they are easily computed and more easily realized in practice than optimal plans which tend to be difficult to calculate and to call for spreading impractically small amounts of effort over large areas.     

A backward recursive technique for optimal sequential sampling plans

This paper presents a procedure akin to dynamic programming for designing optimal acceptance sampling plans for item-by-item inspection. Using a Bayesian procedure, a prior distribution is specified, and a suitable cost model is employed depicting the cost of sampling, accepting or rejecting the lot. An algorithm is supplied which is digital computer oriented.     

Strong turnpike policies in the single-item capacitated lot-sizing problem with periodical dynamic parameter

This article considers optimization problems in a discrete capacitated lot sizing model for a single product with limited backlogging. The demand as well as the holding and backlogging costs are assumed to be periodical in time. Nothing is assumed about types of the cost functions. It is shown that there exists an optimal infinite inverse policy and a strong turnpike policy. A forward algorithm for computing optimal policies relative to the class of batch ordering type policies is derived. Some backward procedure is adopted to determine a strong turnpike policy. The algorithm is simple, and it terminates after the a number of steps equal to the turnpike horizon. Some remarks on the existence of rolling horizontal plans and forecast horizons are also given. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44: 775–790, 1997     

Design of accelerated life testing plans under multiple stresses

Accelerated life testing (ALT) using multiple stresses is commonly used in practice to resemble the operating stresses at normal operating conditions and obtain failure observations in a much shorter time. However, to date, there is little research into the theory of planning ALT for reliability estimation with multiple stresses. ALT with multiple stresses can result in a large number of stress‐level combinations which presents a challenge for implementation. In this article, we propose an approach for the design of ALT plans with multiple stresses and formulate multistress test plans based on different objectives and practical constraints. We develop a simulated annealing algorithm to efficiently determine the testing plan parameters. We demonstrate the proposed method with examples based on an actual test conducted using three stress types. The obtained optimal test plans are compared with those based on fractional factorial design. © 2013 Wiley Periodicals, Inc. Naval Research Logistics 60: 468–478, 2013     

Optimal design of accelerated life tests with two stresses

Most of the previous works on designing accelerated life test plans were concerned with the case where a single stress is employed for acceleration. In this article we develop optimal accelerated life test plans when two stresses are involved with possible interaction between them. The lifetimes of test items are assumed to follow an exponential distribution, the mean of which depends on the stresses according to the generalized Eyring law. A factorial arrangement of test points is considered for an efficient utilization of equipment, and the low level of each stress and the proportion of test items allocated to each test point are determined such that the asymptotic variance of the maximum-likelihood estimator of the mean lifetime at the use condition or of an acceleration factor is minimized. Patterns of optimal plans are identified and their efficiencies are compared with the corresponding single-stress accelerated life test plans. © 1996 John Wiley & Sons, Inc.     

Economic design of sampling plans with multi-decision alternatives

For situations where there are several markets with different profit-cost structures, economic attributes sampling plans are developed for determining the market to ship the lot to. Two sampling plans are considered; the fixed-size sampling plan with several levels of acceptance numbers, and the inverse sampling plan with several levels of sample sizes. Linear profit models are constructed which involve four profit/cost components; profit from a conforming item, inspection cost, replacement cost, and cost from an accepted nonconforming item. For fixed-size and inverse sampling plans, methods of finding optimal sampling plans are presented and examples with beta-binomial prior distributions are given.     

A multifacility capacity expansion model with joint expansion set-up costs

This article describes a multifacility capacity expansion model in which the different facility types represent different quality levels. These facility types are used to satisfy a variety of deterministic demands over a finite number of discrete time periods. Applications for the model can be found in cable sizing problems associated with the planning of communication networks. It is assumed that the cost function associated with expanding the capacity of any facility type is concave, and that a joint set-up cost is incurred in any period in which one or more facilities are expanded. The model is formulated as a network flow problem from which properties associated with optimal solutions are derived. Using these properties, we develop a dynamic programming algorithm that finds optimal solutions for problems with a few facilities, and a heuristic algorithm that finds near-optimal solutions for larger problems. Numerical examples for both algorithms are discussed.     

多传感器多目标定位与跟踪技术研究

针对炮兵打击目标的特性和获取目标信息所采用的侦察设施 ,研究了多传感器多目标定位和跟踪问题。在闭圆和聚类概念的基础上 ,提出了一种多传感器多目标融合算法 ,并给出了状态估计的最优解。仿真结果证明了这种算法的有效性。这一模型的物理实现正在进一步研究之中。     

基于可拓方法的C3I作战方案生成与评价

作战指挥决策支持系统是指挥自动化系统的重要组成部分,作战方案生成与评价是作战指挥决策支持系统的基本功能.根据作战指挥决策支持系统特点将可拓方法应用于作战方案生成与评价,并分析了其优势所在.结合空战案例运用发散树方法进行作战方案集的开拓,并利用优度评价方法进行作战方案的评价,从而得到最佳作战方案.     

基于CPSO算法的海空跨域无人航行器集群协同作业路径规划

针对海空跨域无人航行器集群在复杂水域环境下协同作业以追踪水下目标的任务,提出一种基于协同粒子群(CPSO)的协同作业路径规划算法.考虑不同无人航行器集群特性优势,合理分解并分配远距离追踪水下目标任务过程,并利用CPSO算法进行路径规划.在CPSO算法中,首先为无人机(UAVs)集群规划飞行路径,UAV飞行过程中探测水面...     

Optimal motion planning in rapid‐fire combat situations with attacker uncertainty

This article provides a modeling framework for quantifying cost and optimizing motion plans in combat situations with rapid weapon fire, multiple agents, and attacker uncertainty characterized by uncertain parameters. Recent developments in numerical optimal control enable the efficient computation of numerical solutions for optimization problems with multiple agents, nonlinear dynamics, and a broad class of objectives. This facilitates the application of more realistic, equipment‐based combat models, which track both more realistic models, which track both agent motion and dynamic equipment capabilities. We present such a framework, along with a described algorithm for finding numerical solutions, and a numerical example.     

An approach to modeling electric utility capacity expansion planning

This article describes an algorithm for solving the static electric utility capacity expansion problem. The advantages of this algorithm are twofold. First, it is simpler and yet more efficient than previous algorithms for the same problem. Second, by making simplifying but realistic assumptions on plant sizes it is possible to use this algorithm for the case where one does not allow fractional plant additions. While the model has n variables, it has a clear two-dimensional geometric representation for understanding its properties, developing an algorithm, and interpreting the optimal solution. This algorithm has been implemented in the Intermediate Future Forecasting (IFFS) capacity expansion model at the Department of Energy.     

基于DCSP的编队武器兼容性约束协调

编队武器兼容性约束协调,是一个典型的求解分布式约束满足问题的过程。针对这一特点,建立了编队武器兼容性约束满足问题模型,提出了一种基于异步回溯的分布式约束满足算法。该算法运用异步回溯获得一个初始可行解,然后以作战效能最优为原则增添新的方案,并进行约束一致性检查,最终得到满意的编队武器运用方案。仿真验证了算法的可行性。     

Optimal replacement policies for multistate deteriorating systems

We consider state-age-dependent replacement policies for a multistate deteriorating system. We assume that operating cost rates and replacement costs are both functions of the underlying states. Replacement times and sojourn times in different states are all state-dependent random variables. The optimization criterion is to minimize the expected long-run cost rate. A policy-improvement algorithm to derive the optimal policy is presented. We show that under reasonable assumptions, the optimal replacement policies have monotonic properties. In particular, when the failure-rate functions are nonincreasing, or when all the replacement costs and the expected replacement times are independent of state, we show that the optimal policies are only state dependent. Examples are given to illustrate the structure of the optimal policies in the special case when the sojourntime distributions are Weibull. © 1994 John Wiley & Sons, Inc.     

Lot sizes under continuous demand: The backorder case

We study a deterministic lot-size problem, in which the demand rate is a (piecewise) continuous function of time and shortages are backordered. The problem is to find the order points and order quantities to minimize the total costs over a finite planning horizon. We show that the optimal order points have an interleaving property, and when the orders are optimally placed, the objective function is convex in the number of orders. By exploiting these properties, an algorithm is developed which solves the problem efficiently. For problems with increasing (decreasing) demand rates and decreasing (increasing) cost rates, monotonicity properties of the optimal order quantities and order intervals are derived.     

Optimal timing schedules in earliness-tardiness single machine sequencing

The article deals with a single machine earliness-tardiness scheduling model where idle times are permitted in job processing. Based on a cluster concept we develop properties of the model that lead to a very fast algorithm to find an optimal timing schedule for a given sequence of jobs. The performance of this algorithm is tested on 480 randomly generated problems involving 100, 200, 400 and 500 jobs. It takes less than two seconds to solve a 500 job problem on a PC. © 1995 John Wiley & Sons, Inc.     

Optimal design of accelerated life testing plans for periodical replacement with penalty

Accelerated life testing (ALT), enhanced by optimal test plans, has been widely accepted in practice as a quick approach for estimating the reliability of a product. From the estimation result, preventive maintenance schedules can be determined to ensure the performance of the product under its normal operating conditions. By default, maintenance decision‐making is regarded as the last and least rewarding step. However, sometimes the maintenance schedules, such as preventive maintenance intervals, are predetermined due to customer concerns and/or by various mandatory regulations and rules. Under such circumstances, how to accurately estimate the expenditure (e.g., on maintenance or spare parts management) associated with these maintenance requirements becomes an important issue. A viable solution is to incorporate the maintenance requirements into ALT plans. This paper provides an approach for the optimal design of ALT plans oriented by a mandatory periodical replacement schedule subject to a discounted penalty. The objective is to improve the estimation accuracy of the economic impact of this maintenance requirement. A numerical experiment is provided to demonstrate the approach in practical use. © 2008 Wiley Periodicals, Inc. Naval Research Logistics 2009     

Optimal resource extraction with uncertain reserves

We consider the problem of finding a plan that maximizes the expected discounted return when extracting a nonrenewable resource having uncertain reserves. An extraction plan specifies the rate at which the resource is extracted as a function of time until the resource is exhausted or the time horizon is reached. The return per unit of resource extracted may depend on the rate of extraction, time, and the amount of resource previously extracted. We apply a new method called the generalized search optimization technique to find qualitative features of optimal plans and to devise algorithms for the numerical calculation of optimal plans.