製程能力指標Yq/Y複式抽樣之信賴下限

Abstract

製程能力指標已廣泛被用來衡量製程的能力與產品的品質，製程良率 是常見被製造業用來判斷製程好壞的標準；品質良率 則是進一步將顧客損失考慮在內。本篇論文則是提出一個新指標 ，屏除製程不良品的部份，直接考慮顧客接收到的良品，再計算其完全滿足顧客要求的產品比例。為一個更站在顧客角度，提供顧客更直接判斷所接收產品好壞的指標。然而 之估計值與其統計性質要以數學來推導表達是非常窒礙難行，因此製程能力的檢定也就無法執行。我們運用複式抽樣，一種無母數而大量運用電腦運算的方法來求得 的信賴下限，以達到檢定的目的。在本論文中介紹四種複式抽樣方法所建構的信賴下限，在五種不同母體分配（一個常態分配與四種非常態分配）的環境下做模擬，包括對不同參數（如 的實際值、製程偏移程度與各分配的母體參數等）設定不同水準，做一些統整與分析，比較四種複式抽樣信賴下限的好壞。最後也舉應用在背光模組製程的例子來說明如何使用 指標及複式抽樣方法求得的信賴下限，如此便可以判斷產品是否有達到原訂的水準。

Process capability indices are widely used in manufacturing industrial to provide a numerical measure on whether or not a process is capable of producing items that meet a preset quality requirement. Process yield is the most common criterion used in the manufacturing industry for measuring process performance; Quality yield goes a step further to take customer loss into consideration. This thesis introduce a new index ,which only considers the conformed products customer receives rather than the proportion of non-conformed products of the manufacturing process, and quantifies how close a product that customer has received meets 100% customer satisfaction. The index can provide a judgment to the process from the customer’s viewpoint. However statistical properties of the estimated are mathematically intractable. Therefore, capability testing can not be performed. We use a nonparametric but computer intensive method called bootstrap to obtain a lower confidence bound on for capability testing purposes. Four types of bootstrap lower confidence bounds are introduced and simulating for five distributions (one normal and four non-normal) with different true values of , the degree the process mean shifts from the target and population parameters are conducted. Then a comparison is made of the performances of the bootstrap and the parametric estimates. An application using the index and the bootstrap lower confidence bounds for the backlight modules manufacturing process is presented for illustration purposes.