Browsing by Author "Chapman, Stephen Clay"

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    The economic design of multivariate acceptance sampling plans
    Chapman, Stephen Clay (Virginia Polytechnic Institute and State University, 1972)
    A total expected cost model for multivariate acceptance sampling is developed. The components of cost included in the model are presented in two phases: the cost of making the quality control decision (sampling inspection) and the cost of implementing the quality control decision (accept the inspection lot, scrap the lot, or screen the lot). Several variables are to be controlled within their given specification limits, where the sample mean for each of the variables in the criterion by which lot acceptance for that variable is determined. The decision variables are the sample size and the lower and upper control limits for each of the characteristics subjected to the control. The pattern search is used to determine the values of the decision variables which minimize the total expected cost of quality control per inspection lot submitted for control. The lot mean, sample mean, and individual unit measurements for each of the quality characteristics are considered to be random variables. Sensitivity analysis is performed to determine the robustness of the model to changes in the form of the distributions on the lot means given that the desired mean and variance of these distributions has been accurately estimated.
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    Probabilistic formulations of some facility location problems in discrete space
    Chapman, Stephen Clay (Virginia Tech, 1975-05-04)
    The first formulation to be examined is a probabilistic version of the set covering problem. The problem can be stated as follows: determine the locations of the minimum number of facilities among a discrete set of feasible location sites in order to assure that the probability each customer is covered by some facility is no less than a specified value. The second problem treated involves the location of a given number of facilities among a discrete set of feasible location sites in order to maximize the minimum probability that a customer is covered by some facility. This problem is a probabilistic formulation of a special case of the discrete space, minimax location problem known as the p-center problem. Thus, the first and second problems can be considered to be complementary problems. Frequently, several measures of overall system effectiveness must be considered simultaneously. This is particularly the case in many public sector location problems. Thus, the third problem treated in the dissertation considers the case in which several objectives are to be optimized collectively. The problem is formulated as a goal programming problem in which the objectives are ranked ordinally. The problems discussed above are formulated probabilistically under the assumption of a discrete solution space. This approach was taken in order to account explicitly for the random variation inherent in the systems of inte~est. Example problems are employed throughout the research to assist in the explanation of each formulation. The emphasis in the research is placed upon a sound formulation of each problem, reduction of the problem to an equivalent but computationally more efficient formulation, and the application of an appropriate procedure in solving each problem. Sensitivity analyses are conducted in order to provide further insight into the specific cause-effect relationships.