貝氏方法應用於計量型戴明檢驗模式之研究

Bayesian Analysis of Deming's Inspection Model using Variables Sampling

陳慧雯(Hui-Wen Chen)

指導教授 ： 徐旭昇

元智大學/工程學院/工業工程與管理學系/碩士(2003年)

摘要

本論文旨在提供製造商計量模式適用於其產品屬於可拆解再裝配狀況時，該如何進行進料抽樣檢驗及如何選擇組件供應商。針對兩種組件規格(1)雙邊規格及(2)單向規格，就戴明成本模式發展貝氏計量型檢驗計劃。研究模式假設情況是依據資料的分析，在雙邊規格限制下，可以假設組件功能值為常態分配但期望值未確定；而單向規格則假設功能值為指數分配同時期望值亦未確定。模式成本考慮的範圍涵蓋組件之檢驗成本、不良品所發生之額外檢驗成本及其所導致產品失效成本，而以最小期望成本為目標。以辛普森3/8法則來計算數學模式中之積分值，利用二分法求算出最小期望損失成本，並以Visual Basic語言撰寫程式來執行模式之數學運算。在相同假設條件下比較戴明模式在以貝式方法計算計量型與計數型，與傳統方法計算計數型三種情況作比較。結果發現，貝式計量型之成本與抽樣數皆比貝式計數型來得低，同時兩者之成本皆比傳統方法計算計數型來得低。最後，本研究對模式之相關參數諸如檢驗成本、驗前分配、與批量大小做敏感度分析。

關鍵字

貝氏決策方法 ； 計量型抽樣檢驗計劃 ； 計數型抽樣檢驗計劃

並列摘要

This thesis studies a sampling inspection model discussed by Deming that can be applied to a situation where the quality characteristic measurement of items is on a continuous scale. In previous studies the model was discussed on the case of attributes sampling plan; i.e., sampling information is concerning the number of items being conforming or nonconforming. This study develops a variable sampling plan under the framework of Deming’s model using Bayesian approach with the objective to minimize the Bayes’ risk. We first derive the model from a general point of view and then discuss the model for two particular cases: one is double-sided specification limits with component performance assumed to be normal distribution and the other is single-sided specification limit with exponential distribution. For both cases the unknown parameter is mean. The models by attributes for both cases under the same probability model and cost structure are also derived and analyzed. In the numerical result we find that the sampling model by variables needs less samples and produces less cost than the model by attributes. We also conclude that the expected total cost of the model is smaller under Bayesian approach as compared to directly applying the Deming’s rule with classical approach. Finally, a sensitivity analysis on an example is presented in order to realize the effects of model parameters such as inspection cost, prior distribution, and lot size on the total cost and the optimal sample size of the problem.

並列關鍵字

Bayesian Decision Analysis ； Sampling Plan by Variables ； Sampling Plan by Attriables

參考文獻

16. 林世偉，「不可修復產品原料供應商之選擇─貝氏決策模式」，元智大學工業工程研究所碩士論文，1998年6月。

18. 邵嘉瑀，「變異數不確定下計量型戴明抽樣檢驗模式之貝氏分析」，元智大學工業工程研究所碩士論文，2002年6月。

15. 林鴻欽，「貝氏檢驗計劃之設計」，元智大學工業工程研究所碩士論文，1992年6月。

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