多條生產線製程下Cpu之信賴下界與允收抽樣

Abstract

允收抽樣計畫是統計品管中之重要領域。允收抽樣計畫是指自貨批中隨機抽取部分樣本檢驗，在買賣雙方願意承擔的風險下，根據樣本評估之結果，來決定一批產品是否能被允收，許多研究都曾對允收抽樣計畫做過討論，但大部分的研究都著重在單條生產線的製程。現今高科技製程具有多條生產線是常見的現象，Pearn (2015) 等學者們將 Cpu 推廣至多條獨立生產線製程上，新定義一個指標 CpuM，並提供了估計量 CpuMhat 的常態近似分配以及信賴下界。本研究透過資料模擬的方式，檢驗此常態近似分配之準確性，此外，我們應用製程能力指標 CpuM 來處理單邊規格產品在多條生產線製程下的允收決策。為了方便業界使用，我們列出在不同的生產者、消費者風險下，所需抽檢之產品樣本數及產品允收臨界值，業者可利用本篇研究的成果做出更有效的決策。

In statistical quality control, acceptance sampling plan is an important problem of product sentencing, which provides a decision rule for accepting or rejecting a production lot, under the designated risks given by the producer and consumer. Acceptance sampling plan has received substantial research attention but restricted to single manufacturing line process. Nowadays, multiple manufacturing lines are common for high-technology processes. Pearn et al. (2015) extend Cpu to a new index CpuM for processes with multiple lines. A natural estimator of CpuM is provided and a normal approximation to its distribution and lower confidence bound, are derived. In this thesis, the accuracy of the normal approximation is studied by simulation. Moreover, we apply the index CpuM to deal with product sentencing for one-sided processes with multiple manufacturing lines. For the convenience of industry applications, we tabulate the required sample size and the corresponding critical acceptance value for various alpha-risks, beta-risks, the manufacturing lines k , the capability requirements acceptance quality level (AQL), and the lot tolerance percent defective (LTPD). Practitioners can use the proposed method to make reliable decisions.