使用個別誤判誤差的篩選程序之研究

因為有些產品的品質特性檢查困難、昂貴或是具有退化性，因此藉由觀察數個和表現變數有關的篩選變數，由它們來判定產品是否被接受。此方法稱之為篩選程序。為了節省檢驗成本和檢驗時間，因此進一步發展出循序篩選程序。本論文主題主要是針對使用個別誤判誤差的循序篩選程序之研究。本研究提出一修正單邊循序篩選程序和一修正雙邊循序篩選程序來簡化舊的循序篩選程序。我們以原油提煉汽油的例子來做新法和舊法的數值比較，結果顯示新法的期望成本非常接近舊法或比舊法好。所以我們推薦使用新法，因它有不用加權兩次較為簡化的優點，且其成本表現也比舊法好。對修正的循序篩選程序，我們考慮三種品質成本函數的期望總成本，其中期望總成本是總檢查成本、期望拒絕成本和期望品質成本的總和。當數個篩選變數配置在多站時，我們可推導出所有所需要的機率和三種總期望成本的一般化公式。因此，即使是三站以上的篩選程序，所需要的機率和成本都可以推導求得。並以最小期望總成本為準則來找出最適配置。最後，我們給兩個例子來示範本研究所提出之修正循序篩選程序在三種總期望成本下之最適配置的選擇。

關鍵字

平均出廠品質；期望品質成本；個別誤判誤差機率；多變量常態分配；循序篩選程序

並列摘要

Since the measuring on the quality characteristics of some products may be hard, expensive or degenerative, the item is determined to be accepted or not based on the observed screening variables which are correlated with the performance variable. The screening procedure is thus arisen. In order to reduce the cost and time effort of inspection, a sequential screening procedure is developed. This dissertation is focusing on the study of the sequential screening procedure based on the individual misclassification error. We propose a modified one-sided sequential screening procedure and a modified two-sided sequential screening procedure to simplify the existing procedures. We use the example of refining gasoline from the available crude oil to do the numerical comparison of the new method and the old method, and the results show that the modified sequential screening procedure performs very close to or better than the old one. Since the new method has the advantage of simplifying the old method by only weighting the screening variables once instead of weighting twice and has better performance than the old method, the new method is recommended for use. For the modified screening procedures, we also consider the expected total costs of three kinds of quality cost functions based on the individual misclassification error, where the expected total cost is the sum of the total inspection cost, the expected cost of rejection and the expected cost of quality. We derive the generalized computational formulas for the desired probability quantities and three kinds of expected total costs when k screening variables are allocated into r stages, where r and k are positive integers, k≦r and r can be more than 3. The criterion of minimum expected total cost is used to search for the optimal allocation. At last, we give two examples to illustrate the selection of the optimal allocation combination for the sequential screening procedure under three kinds of expected total costs.

並列關鍵字

Average outgoing quality ； Expected cost of quality ； Individual nonconforming probability ； Multivariate normal distribution ； Sequential screening procedure

參考文獻

Tsai, H. T., Chang, P. L. and Lu, K. H. (1992). A study of using multiples screening variables on double screening procedure. Journal of the Chinese Institute of Industrial Engineers, 9(1), 45−53.

Bai, D. S., Kim, S. B. and Riew, M. C. (1990). Economic screening procedures based on correlated variables. Metrika, 37(1), 263−280.

Li, L. and Owen, D. B. (1979). Two-sided screening procedures in the bivariate case. Technometrics, 21(1), 79−85.

Lipow, M. and Eidemiller, R. L. (1964). Application of the bivariate normal distribution to a stress vs strength problem in reliability analysis. Technometrics, 6(3), 325−328.

Madsen, R. W. (1982). A selection procedure using a screening variate. Technometrics, 24(4), 301−306.

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使用個別誤判誤差的篩選程序之研究

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