貝氏逐次抽樣計畫與傳統逐次抽樣計畫之比較分析

Study on Bayesian Sequential Sampling Plan Compare with Classical Sequential Sampling Plan

黃允成(Yun-Cheng Huang) ； 林淑萍(Shu-Ping Lin) ； 蘇琬菁(Wang-Jing Su) ； 黃彥彰(Yan-Zhang Huang)

《管理研究學報》 9卷 (2009/12) Pp. 1-44

https://doi.org/10.6626/MR.2009.9.01

摘要

本文是針對破壞性檢驗進行研究，同時納入檢驗成本及因抽樣誤差所造成之誤判損失成本下，以貝氏估計法求得母體不良率之後驗機率，建構出期望總品質成本函數，並經由電腦數值分析，求出在期望總品質成本最小下之最適抽樣個數。此外，再運用逐次抽樣方法，即可在每一逐次抽驗中，決定是否要停止抽樣，或是繼續抽樣後再做決策，以建構出逐次抽樣決策圖。最後，舉一數值範例與傳統逐次抽樣計畫進行比較及分析，以驗證本研究之貝氏逐次抽樣計畫是否優於傳統逐次抽樣計畫。

關鍵字

貝氏定理 ； 破壞性檢驗 ； 逐次抽樣 ； ML-Ⅱ

並列摘要

In this paper, we focus our attention on sample size for destructive inspection and use ML-Ⅱ to estimate the upper limit of the Prior pdf for defective rate of populaton. After that, we consider inspection cost and losses of sampling error and we use Bayesian estimation method for expected total losses. Applying computerized numerical analysis method, we can find out the optimal sample size to minimize the total losses. Furthermore, we use the concept of sequential sampling, then we draw a sample, and inspect it in each sequential observation to determine whether to stop sampling and then making decision or not, to construct the decision chart of sequential sampling. In order to test and verify whether the Bayesian sequential sampling plan is superior to classical sequential sampling plan, we proposed a numerical example to carry on the comparison. Finally, we derived the concrete conclusions for future studies and practical applications.

並列關鍵字

Bayesian theorem ； Destructive inspection ； Sequential sampling ； ML-Ⅱ