以複式模擬法建構兩個皮爾森分配製程之製程能力指標C''pmk差異值之信賴區間

Abstract

企業為了追求良好的產品品質以提昇產品的競爭力，常使用製程能力指標來比較兩個製程或供應商的優劣。目前所發展出來的製程能力指標有非常多，其中C"pmk可應用在對稱及非對稱規格區間及皮爾森家族分配（Pearson Family Distribution）製程，應用價值較其他指標為高，故本論文使用製程能力指標C"pmk，來作為評比兩個供應商或製程的依據。但因為製程能力指標C"pmk的分配過於複雜，目前尚未有學者推導出來，因此無法進行兩製程的假說檢定以比較其優劣，而若以單一抽樣之樣本直接計算兩製程的C"pmk作比較，則會因為點估計之抽樣誤差而使評比結果失真。基於以上考量，本論文使用複式模擬法（Bootstrap Simulation）之BCa信賴區間估計法，以少量樣本模擬母體參數分配，進而求算出兩個製程之製程能力指標C"pmk差異值的信賴區間，以正確判斷兩個製程的優劣。本論文最後並將兩個製程或供應商優劣的評比流程寫成應用程式，讓沒有統計背景的工程人員也能夠快速且正確地得到評比結果。

Process capability analysis is an important tool for enhancing the competitiveness of product/process. Manufacturers usually utilize process capability index (PCI) to compare the process capabilities of two processes or suppliers. Many process capability indices are developed based on a normal process with symmetric specification limits. Only few indices can be utilized to evaluate a non-normal process or a normal process with asymmetric specification limits. Among all the PCIs, C"pmk index is most applicable. It can be employed in a normal or non-normal process with symmetric or asymmetric specification limits. However, the exact probability distribution of C"pmk is too complicated to be derived, and consequently, the related hypotheses testing and confidence interval concerning C"pmk cannot be developed. Therefore, this study proposes a method to utilize Bootstrap simulation to construct a confidence interval for the difference between two true capability indices C"pmk for processes possessing Pearson family distribution with asymmetric or symmetric specification limits. The proposed Bootstrap confidence interval for the difference between two capability indices C"pmk can be used to effectively determine which process or manufacturer has a better production capability. Moreover, the computer program is also provided for the proposed for practitioners with little statistical background to use.