對稱與非對稱規格製程準確性之估計與檢定

Abstract

Pearn (1998)提出製程準確性指標 來衡量製程的集中程度(群集於中心之能力)。在本篇論文中，我們根據估計量 之明確累積分配函數(CDF)推導 估計量之統計特性。藉由臨界值、P值和最低信賴區間值之計算，我們發展出檢測製程準確性之方法。除此之外，為了使工廠製程量測員更容易量測產品之製程準確性，我們進一步將衡量製程準確性指標 推廣到非對稱規格之製程，並找出非對稱規格製程準確性指標的估計值 。工廠製程量測員根據附錄裡的製程指標表格，就能快速地作出可信賴的決策與評估產品的製程品質是否需要馬上改善。在論文的最後，我們用三個實際例子來說明如何估計與檢定製程準確性。

Pearn et al. (1998) introduced the process accuracy index to measure the degree of process centering (the ability to cluster around the center). In this paper, we derive an explicit form for the cumulative distribution function of the estimator . Subsequently, the distributional and inferential properties of the estimated process accuracy index are provided. Calculations of the critical values, p-values, and lower confidence bounds are developed for testing process accuracy. Further, a generalization of for cases with asymmetric tolerances is proposed to measure the process accuracy. The distributional properties of the corresponding natural estimator are investigated. Based on the results practitioners can easily perform the process accuracy testing, and make reliable decisions on whether actions should be taken to improve the process quality. Three application examples are given to illustrate how we test process accuracy using the actual data collected from the factory.