雙邊規格製程能力指標Spk的信賴下界

Abstract

在製造工廠內，製程良率被當成標準的衡量準則已經很久。製程能力指標 可以精確地衡量常態性分配製程的良率。然而，欲以精確的數學方式推論得到 的自然估計之抽樣分配卻相當困難，因為該抽樣分配非常複雜。因此，多種近似估計方法都被開發，試圖解決以上難題。Pearn et al. (2010)利用二階條件泰勒展開式推導出一個近似估計量，他們利用臨界值(critical value)深入探討該近似估計量的性質。Chen (2005)則是利用拔靴法，模擬產生四種不同的信賴下界(the standard bootstrap (SB), the percentile bootstrap (PB), the biased-corrected percentile bootstrap (BCPB), and the bias-corrected and accelerated bootstrap (BCa))。Chen(2005)認為SB信賴下界比起其他三個信賴下界具有更高的涵蓋率，也就是說，SB信賴下界的績效優於其他三種拔靴法。這篇碩士論文中，我們比較Pearn et al. (2010)的近似估計量所產生的信賴下界，還有四種拔靴法(SB, PB, BCPB, and bootstrap-t (BT) methods)產生的信賴下界。實驗結果顯示Pearn et al. (2010)所產生的信賴下界有幾個優點：(1)在五種信賴下界中，其具有最高的涵蓋率，這也是最重要的優點，(2)Pearn et al. (2010)提出的是一種可解析函式(analytical function)，由此可知，由此法產生的信賴下界所存在的誤差能夠被衡量，但是拔靴法地信賴下界卻無法衡量誤差(3)Pearn et al. (2010)提供唯一的信賴下界，但是拔靴法提供振動的信賴下界且無法預測。綜合以上理由，我們認為由Pearn et al. (2010)所產生的信賴下界比起拔靴法更優良。

Process yield has been a common and standard criterion in manufacturing industry for a long time. The yield index provides an exact measure on the production yield of normal processes. However, the sampling distribution of estimated is analytically intractable, therefore the approximating approach is considered. Chen (2005) applied the famous boot-strap method, a nonparametric but effective simulation technique, to deal with the intractabil-ity. Chen (2005) utilized four bootstrap methods to conduct lower confidence bound (LCB) and noted that the standard bootstrap (SB) method outperforms the other three in coverage proportion. Moreover, Pearn et al. (2010) used the convolution method based upon the se-cond-order approximation by Taylor expansion to estimate the yield index . In this thesis, we compared coverage proportions and LCBs based on the convolution and the bootstrap approximation. The results revealed that the CP incurred by the LCB obtained from the convolution approximation outperforms the one from the bootstrap method.