產品品質良率與製程損失指標

Abstract

在製造工業對於量測製程績效好壞，製程良率是最為常見的判斷標準。而一個更為先進的測量公式，稱為品質良率指標 Yq，把顧客損失考慮進來。針對任意分配的製程，品質良率指標可以計算製程的品質良率。品質良率的作法是，針對產品品質特性偏離目標值之變異程度，對於良率作一個處罰的動作，也就是把平均的產品損失考慮進來。換句話說，製程良率減掉在規格內的產品損失就是品質良率。製程損失指標 Le 的定義為二次期望損失除以製程規格長度一半的平方。在文獻上，在 Yq 指標的研究侷限於樣本的點估計。決策者可能會對 Yq 的信賴下界有興趣，而不是純粹只有點估計量。另一方面，文獻上大部份在品質保證領域的研究都專注於探討製程規格是對稱的情況。然而，非對稱規格很可能產生於開始時規格是對稱的，但是製程的分配是偏態或是服從非常態分配的情況。在非對稱規格的情況之下，使用傳統的 Yq 和 Le 來衡量製程績效是有風險的，很可能所獲得的結果會使人誤解實際的狀況。本文針對 Yq 指標求取其信賴下界，並且推廣 Yq 和 Le 指標來處理非對稱規格的製程。本文的具體貢獻主要有三方面。第一方面是提出兩個可靠的方法來把 Yq 的點估計值變換成信賴下界，來衡量製程的品質良率。其中一個方法是在常態分配的假設下，針對超低不良率的生產製程品質良率的測量。另一個方法則是針對任意的製程分配，我們提出複式抽樣方法來獲得品質良率的信賴區間下界。第二方面是把傳統的 Yq 和 Le 指標推廣成可以處理非對稱規格的製程。我們在文中證實了此推廣的優點，並且研究非對稱規格的 Yq 和 Le 指標估計量的一些統計性質。第三方面，我們研究了傳統 Yq 和 Le 指標自然估計量的一些統計性質。本文所獲得的研究成果，有助於從事品管工作者對於好的 Yq 和 Le 指標估計量的選擇，並且在評估製程能力提供更有效的決策方式。

Process yield is the most common criterion used in the manufacturing industry for measuring process performance. A more advanced measurement formula, called the quality yield index (Yq), has been proposed to calculate the quality yield for arbitrary processes by taking customer loss into consideration. Quality yield penalizes yield for the variation of the product characteristics from its target, which presents a measure of the average product loss. In other words, quality yield is calculated as process yield minus process loss within the specifications. Process loss index Le is defined as the ratio of the expected quadratic loss to the square of half specification width. In the literature, only sample point estimate for Yq is investigated. The decision maker would be interested in a lower bound on Yq rather than just the sample point estimate. Most research in quality assurance literature has focus on cases in which the manufacturing tolerance is symmetric. However, asymmetric tolerances can also arise in situations where the tolerances are symmetric to begin with, but the process distribution is skewed or follows a non-normal distribution. Under asymmetric tolerances situation, using Yq and Le would be risky and probably the results obtained are misleading. This dissertation focus on obtaining lower bounds on Yq and extending Yq and Le to handle processes with asymmetric tolerances. The concrete contributions of this dissertation are threefold. The first is to propose two reliable approaches for measuring Yq by converting the estimated value into a lower confidence bound. One approach is for production processes with very low fraction of defectives under normality assumption. For arbitrary underlying distributions, we propose a bootstrap approach to obtain lower confidence bound on quality yield. The second is to generalize Yq and Le for asymmetric tolerances. The merit of the generalization is justified, and some statistical properties of the estimated generalization are investigated. The third is to investigate the statistical properties of these natural estimators for Yq and Le. The results obtained in this dissertation are useful to the practitioners in choosing good estimators and making reliable decisions on judging process capability.