Graduate Thesis Or Dissertation
 

Economically optimal control charts for two stage sampling

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https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/8k71nm27q

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  • Control charts are designed to monitor population parameters. Selection of a control chart sampling plan involves determination of the frequency of samples, size of each sample, and critical values to determine when the system is sending an out-of-control signal. Since the main use of control charts is in industry, a widely accepted measure of a good sampling plan is one that minimizes the total cost of operating the system per unit time. Methods for selection of control chart sampling plans for economically optimal X charts are well established. These plans focus on single stage sampling at each sampling period. However, some populations naturally call for two stage sampling. Here, the cost of operating a system per unit time is redefined in terms of two stage sampling plans, and computer search techniques are developed to determine the control chart parameters. First the sample sizes and critical values are fixed, and Newton's method is used to determine the optimal time between samples. Then, a Hooke - Jeeves search is used to simultaneously determine the optimal critical value, sample sizes and time between samples. Adjustment to the latter is required whenever any of the other three parameters change. Alternative methods are also discussed. Information from a single sample is usually used to control shifts in both the process mean and variance. With two stage sampling, this means two additional control charts are used, one for each variance component. The computer algorithm developed for selection of parameters for X charts is adapted by expanding the Hooke Jeeves search region to a six dimensional space, now over three critical values, sample sizes for both stages of sampling, and the time between samples. These methods are applied to a real data set that requires two stage sampling. A representative analysis of the sensitivity of the optimal sampling scheme to the input parameters completes the paper.
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