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.     

Comparative evaluation of prior versus progressive articulation of preference in bicriterion optimization

Procedures for solving multiple criteria problems are receiving increasing attention. Two major solution approaches are those involving prior articulation and progressive articulation of preference information. A progressive articulation (interactive) optimization approach, called the Paired Comparison Method (PCM) is compared to the prior articulation approach of a priori utility function measurement in a quality control decision environment from the perspective of the decision maker. The three major issues investigated included: (1) the ease of use of each method, (2) the preferences of solutions obtained, and (3) the insight provided by the methodology into the nature and structure of the problem. The problem setting involved management students who were rquired to determine an acceptance sampling plan using both methods. The PCM provided the most preferred solutions and was considered easier to use and understand. The prior articulation of preference method was found to give more insight into the problem structure. The results suggest that a hybrid approach, combining both prior preference assessment and an interactive procedure exploiting the advantages of each, should be employed to solve multiple criteria problems.     

An interactive approach to multiple criteria optimization with multiple decision-makers

In this article we propose a formal man-machine interactive approach to multiple criteria optimization with multiple decision makers. The approach is based on some of our earlier research findings in multiple criteria decision making. A discrete decision space is assumed. The same framework may readily be used for multiple criteria mathematical programming problems. To test the approach two experiments were conducted using undergraduate Business School students as subjects in Finland and in the United States. The context was, respectively, a high-level Finnish labor-management problem and the management-union collective bargaining game developed at the Krannert Graduate School of Management, Purdue University. The results of the experiments indicate that our approach is a potentially useful decision aid for group decision-making and bargaining problems.     

An acceptance life test for high-reliability products

This article introduces a replacement life-test procedure for the exponential failure rate: Failure-free operation of a unit for at least t_k consecutive time units is designated a “success”; the acceptance test is passed if and only if the first success is encountered before k unit failures have been recorded. Test plans are presented and the test is compared with the usual time-truncated test and to the truncated sequential probability ratio test. It is shown that this new test has smaller expected test time than the time truncated test when the true failure rate is small relative to the null hypothesized failure rate. Consistency and unbiasedness are proved and methods for making inferences on failure rate are described.     

Exact bayesian estimation of system reliability from component test data

System reliability is often estimated by the use of components' reliability test results when system test data are not available, or are very scarce. A method is proposed for computing the exact posterior probability density function, cumulative distribution function, and credible intervals for system reliability in a Bayesian setting, with the use of components' prior probability distributions and current test results. The method can be applied to series, parallel, and many mixed systems. Although in theory the method involves evaluating infinite series, numerical results show that a small number of terms from the infinite series are sufficient in practice to provide accurate estimates of system reliability. Furthermore, because the coefficients in the series follow some recurrence relations, our results allow us to calculate the reliability distribution of a large system from that of its subsystems. Error bounds associated with the proposed method are also given. Numerical comparisons with other existing approaches show that the proposed method is efficient and accurate. © 1997 John Wiley & Sons, Inc.     

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.     

Technical and proliferation‐related aspects of the dismantlement of Russian Alfa‐Class nuclear submarines

When does a state become a “nuclear weapon state”? How we choose to answer this question has significant implications for proliferation assessment, analysis, and policy. Traditionally, the standard demarcation line has been a state's first nuclear test, but in recent years analysts have increasingly focused instead on the accumulation of a significant quantity (SQ) of fissile material. The article argues that although the test/no-test indicator clearly has problems, its replacement by the SQ/no-SQ indicator would be highly counterproductive. The article instead proposes supplementing the traditional test/no-test indicator with a theory-driven approach that focuses on the incentives and disincentives to test.     

Game theoretic analysis of maximum cooperative purchasing situations

This article introduces maximum cooperative purchasing (MCP)‐situations, a new class of cooperative purchasing situations. Next, an explicit alternative mathematical characterization of the nucleolus of cooperative games is provided. The allocation of possible cost savings in MCP‐situations, in which the unit price depends on the largest order quantity within a group of players, is analyzed by defining corresponding cooperative MCP‐games. We show that a decreasing unit price is a sufficient condition for a nonempty core: there is a set of marginal vectors that belong to the core. The nucleolus of an MCP‐game can be derived in polynomial time from one of these marginal vectors. To show this result, we use the new mathematical characterization for the nucleolus for cooperative games. Using the decomposition of an MCP‐game into unanimity games, we find an explicit expression for the Shapley value. Finally, the behavior of the solution concepts is compared numerically. © 2013 Wiley Periodicals, Inc. Naval Research Logistics 60: 607–624, 2013     

An analysis of the long range operating characteristics of the MIL-STD-105D sampling scheme and some suggested modifications

An integral part of the MIL–STD–105D scheme for sampling inspection by attributes is the transfer from normal inspection to reduced or tightened inspection when the historical record of inspected lots suggests unusually good or bad quality. The switching rules in MIL–STD–105D have been criticized, especially by Japanese manufacturers, as being too severe when what is defined as acceptable quality material is submitted. This paper examines the long range fraction of lots rejected for several MIL–STD–105D sampling plans by using the MIL–STD–105D switching rules, using a modification suggested by the Japanese Standards Association, and by using a second modification developed by the authors. The Japanese Standards Association switching rules are more complex than those in MIL–STD–105D. It is demonstrated that they lead to improved long–range properties for Normal–Tightened–Reduced schemes, but to poorer properties for Normal–Tightened schemes. A simplified set of switching rules is suggested, wherein the “limit numbers” in MIL–STD–105D are eliminated. In comparison to MIL–STD–105D, the simpler rules lead to a lower probability of rejection for good lots and a comparable probability of rejection for bad lots.