The optimum design of multivariate acceptance sampling plans

A model is developed which may be used to determine the expected total cost of quality control per inspection lot under acceptance sampling by variables where several characteristics are to be simultaneously controlled. Optimization of the model is accomplished through the application of a conventional search procedure. The sensitivity of the model and the optimum solution to the shape of the underlying probability distributions is discussed and associated analyses are presented through an example.     

A comparison of several attribute sampling plans

The purpose of this research is to examine several types of procedures for attribute sampling inspection-the widely used Military Standard 105D plans [8], the lesser known Double Zero plans as developed by Ellis [4] and the Narrow Limit gaging plans of Ott and Mundel [9]. Each of the procedures is described with an effort made to illuminate their more subtle features. Then the plans are compared, whence it is revealed that (i) Narrow Limit gaging plans have a serious weakness in comparison to the others and (ii) Double Zero plans tend to be essentially conservative, but that sufficiently tight Military Standard 105D plans can be selected to achieve comparable performance in all ways.     

Continuous sampling plans for markov-dependent production processes

This article discusses the behavior of three continuous sampling plans: continuous sampling plan 1 (CSP 1) and continuous sampling plan 2 (CSP 2) developed by Dodge [5] and Dodge and Torrey [7], and multilevel continuous sampling plan 2 (MLP 2) developed by Lieberman and Solomon [11], when the quality of successive units in a continuous production process follows a two-state time-homogeneous Markov chain. We first derive the average outgoing quality (AOQ) expressions of these plans. Exact procedures for determining the average outgoing quality limit (AOQL) can be obtained only for CSP 1. For CSP 2 and MLP 2 plans, iterative procedures have been used to obtain the AOQL contours. For these plans, it is assumed that the serial correlation coefficient between the two consecutive random variables of the Markov chain is known. In addition, estimation procedures for the coefficient are given. We show that if the serial correlation coefficient of the Markov chain is positive (negative), the AOQL is increased (decreased) as compared to the case when the successive units in the production process follows a Bernoulli pattern. Let r denote the number of production units examined in succession which are found to be of good quality and k denote the inverse of the sampling fraction employed when quality is good. Then if r and k are sufficiently small, it is observed from the graph that, for small departures of the serial correlation coefficient from zero, the AOQL values do not differ significantly for each of the three plans; whereas for sufficiently large values of r and k, the AOQL values differ significantly. Various aspects of these plans, such as their operating characteristics 2 (OC 2) and the serial correlation coefficient, are discussed.     

Minimum cost sampling plans using bayesian methods

This article considers a general method for acceptance/rejection decisions in lot-by-lot sampling situations. Given arbitrary cost functions for sampling, accepting, and rejecting (where the cost can depend on the quality of the item) and a prior distribution on supplier quality, formulas are derived that lead to the minimal cost single-staged inspection plan. For the Bernoulli case, where each item is classified as acceptable or defective, the formulas simplify immensely. A computer code for solving the Bernoulli case is given.     

Toward a determination of optimal multilevel sampling plans

Traditionally continuous sampling plans have been evaluated according to relatively few criteria. These typically include the OC curve (on which AQL systems are based), the ASN, and the AOQ curve. These characteristics are all calculated under the assumption that the process is “in control” so that mathematically they are derived as long-term averages. Thus, any two plans which (long term) spend the same proportion of time on each type of sampling inspection will be identical relative to these criteria. This is true whether sampling from lots or doing unit-by-unit inspection. The goal is to first establish desirable additional criteria and then to develop methods to determine which procedure (of those which satisfy the standard criteria) is optimal relative to the new criteria. To be considered will be measures of a plan's ability to detect a sudden drop in quality (such as ARL).     

The effect of nonnormality on variables sampling plans

Acceptance sampling plans based on variables have been in use for many years. Recently, there has been a renewal of interest in these plans, because of the relative efficiencies that they offer with respect to attributes sampling regarding sample size. Furthermore, in situations where acceptable quality levels are very small, and a high level of protection is desired, variables sampling is often much more efficient than attributes sampling. An important disadvantage of variables sampling is that the distribution of the parameter being inspected must be known. Most standard variables sampling plans assume that the distribution of this parameter is normal. This article examines the effect of the normality assumption in variables sampling. Methods to detect departures from normality are reviewed.     

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.     

Economic screening procedures using a correlated variable with multidecision alternatives

Economic screening procedures using a correlated variable are developed for selecting markets in situations when there are several markets with different profit/ cost structures. It is assumed that the performance variable and the screening variable are jointly normally distributed. Profit models are constructed which involve three profit/cost components: profit from a conforming item, cost from an accepted nonconforming item, and screening inspection cost. Methods of finding the optimal screening procedures are presented and numerical examples are given.     

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.     

The economic effects of inspector error on attribute sampling plans

In this paper the effects of inspector error on a cost-based quality control system are investigated. The system examined is of a single sampling plan design involving several cost components. Both type I and type II inspector errors are considered. The model employs a process distribution, thus assuming that a stochastic process of some kind governs the quality of incoming lots. Optimal plan design is investigated under both error-free and error-prone inspection procedures and some comparisons are made.     

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.     

The incentive effect of acceptance sampling plans in a supply chain with endogenous product quality

This article studies a firm that procures a product from a supplier. The quality of each product unit is measured by a continuous variable that follows a normal distribution and is correlated within a batch. The firm conducts an inspection and pays the supplier only if the product batch passes the inspection. The inspection not only serves the purpose of preventing a bad batch from reaching customers but also offers the supplier an incentive to improve product quality. The firm determines the acceptance sampling plan, and the supplier determines the quality effort level in either a simultaneous game or a Stackelberg leadership game, in which both parties share inspection cost and recall loss caused by low product quality. In the simultaneous game, we identify the Nash equilibrium form, provide sufficient conditions that guarantee the existence of a pure strategy Nash equilibrium, and find parameter settings under which the decentralized and centralized supply chains achieve the same outcome. By numerical experiments, we show that the firm's acceptance sampling plan and the supplier's quality effort level are sensitive to both the recall loss sharing ratio and the game format (i.e., the precommitment assumption of the inspection policy). © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013     

Variable sampling plans for normal distribution indexed by Taguchi's loss function

Taguchi has presented an approach to quality improvement in which reduction of deviation from the target value is the guiding principle. In this approach any measured value x of a product characteristic X brings a loss to consumer in general, where the loss is expressed as a quadratic form with respect to the difference between the measured value x and the target value T of a product characteristic. Then, it is natural to reject the lot which may bring a large loss to consumer. This concept induces us to construct new variable sampling plans based on the Taguchi's loss criterion. In this article, a design procedure of the sampling plans for assuring the loss in the Taguchi's method is proposed. Some numerical results based on the proposed design procedures are illustrated. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44: 591–603 (1997)     

基于元胞数组的多维空间在舰船方案论证设计中的应用

在分析多维空间及元胞数组的基础上,提出了将元胞数组抽象成坐标轴上的点,并以此为基础建立多维空间坐标系.使用多维空间上的离散点来表述水面舰船总体方案设计,用元胞数组来描述组成舰船子系统方案的若干功能属性.该方法将舰船方案用数字化元胞集合表示,集中了基于方案探索的优化论证设计和基于功能积木的虚拟化论证设计的优势.     

On the use of standard tables to obtain Dodge-Romig LTPD sampling inspection plans

Procedures are described which yield single and double sample Dodge-Romig [1] lot tolerance percent defective (LTPD) rectifying inspection plans. For the determination of such plans only a desk calculator and standard tables of the discrete probability distributions are required. Some advantages gained by using these procedures rather than the Dodge-Romig table include: (a) The Consumer's Risk is not limited to 0.10. (b) More choices of LTPD are available. (c) Smaller average total inspection is achieved by using a plan designed for specific “process average” and lot size rather than a compromise plan designed to cover intervals on these two parameters.     

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     

Risk preference,multiple attributes,and multiple criteria in bayesian acceptance sampling plans

Although there has been considerable research directed toward developing Bayesian acceptance sampling plans, little consideration has been given to incorporating a decision-maker's risk attitude or treating such problems in terms of multiple-type defects and multiple criteria. We review our own work which is focused on the above issues. A model incorporating risk preference is shown to yield substantial differences in the characteristics of an optimal sampling plan relative to a typical Bayesian linear cost (risk neutral) model. Bayesian models and optimization schemes for a variety of multiple-type defect plans are reviewed. A bicriterion acceptance model, employing average outgoing quality and average inspection cost is also formulated. Traditional versus interactive optimization procedures are compared empirically in terms of ease of use, satisfaction with solutions, and insight gained into the problem.     

Optimal Bayesian single-sampling attribute plans with modified beta prior distribution

In this article we study the properties of the optimal Bayesian single-sampling plans when the prior distribution of the lot fraction defective is modified Beta, which has been found useful in the analysis of inspection schemes for complex production systems. These properties are used to devise an improved and more efficient algorithm for the determination of the optimal sampling plans. Numerical examples are presented to illustrate the potential computational savings of the algorithm.     

Economic design of X¯ control charts for two manufacturing process models

Control charts are widely used for process surveillance. The design of a control chart refers to the choice of sample size, the width of the control limits, and the interval between samples. Economic designs have been widely investigated and shown to be an effective method of determining control chart parameters. This article describes two different manufacturing process models to which the X¯ control chart is applied: The first model assumes that the process continues in operation while searches for the assignable cause are made, and the second assumes that the process must be shut down during the search. Economic models of the control chart for these two manufacturing process models are developed, and the sensitivity of the control chart parameters to the choice of model is explored. It is shown that the choice of the proper manufacturing process model is critical because selection of an inappropriate process model may result in significant economic penalties.