臺灣博碩士論文加值系統

在高科技產業時代，產品品質的良窳是提昇產品競爭力的一個很重要的因素。許多企業應用統計手法為其產品製程的品質把關，其中最常用到的工具就是製程能力分析。在分析製造商的製程能力時，製程能力指標扮演了一個將製造產品之能力量化的角色。製程能力指標發展至今常見的有Cp、Cpk、Cpm和Cpmk等，其中Cp和Cpk由於觀念簡單且易於計算，已成為目前業界最常使用的製程能力指標。
一般在建構製程能力指標時，必須假設製程母體的分配為常態分配。因此，當製程母體的分配為非常態時，若仍以常態假設下的製程能力指標來評估製程之能力時，將會導致指標值失真。而在真實製程方面，時常會出現製程品質特性資料為非常態分配的情形，譬如混線生產、電子產品的壽命等，其品質特性皆屬於非常態分配。基於傳統製程能力指標在非常態下可能失真的情況，有學者在皮爾森家族分配的假設下，以百分位數法將傳統之製程能力指標Cp和Cpk轉換成非常態製程能力指標CNp和CNpk。針對具雙邊規格之非常態分配的製程能力指標CNpk而言，由於其估計式之機率分配的推導過於複雜，其機率分配迄今尚未能推導出，故與CNpk相關的假說檢定與信賴區間尚未能被發展出來。
由於製程能力分析常用來評估及比較兩個製造商之優劣，以作為下訂單之依據，因此如何發展一套可以正確評估兩個製程能力指標差異值的統計方法是非常重要的。因此，本研究之主要目的即是針對具雙邊規格之非常態製程以複式模擬法來建構兩個非常態製程能力指標CNpk差異值之100（1-α）%信賴區間，以此信賴區間來評估兩個製程或供應商製程能力之優劣。本研究最後亦將此信賴區間建構流程撰寫成簡單之應用流程，並以一實例說明如何應用，以供業界沒有太多統計背景之工程人員使用，藉此流程可簡單快速地構建出兩個CNpk差異值之信賴區間，然後用以正確判斷兩個製程或供應商之優劣。

Process capability index is a highly effective means of evaluating process performance and product quality. Among many developed process capability indices, Cp and Cpk are two most popular indices adopted by industry.
Engineers heavily emphasize applicability and accuracy when using a process capability index to evaluate how a process performs. However, using conventional process capability index Cpk to evaluate a non-normal distribution process often leads to inaccurate results. Therefore, this study presents an appropriate process capability index CNpk to evaluate non-normal distribution processes. Clements method is adopted to adjust the conventional index Cpk. However, the exact probability distribution of CNpk is too complicated to be derived, only the approximate probability distribution of the estimator of CNpk, , can be derived. Consequently, the related hypotheses testing and confidence interval can not be developed. For this reason, the application of CNpk is limited.
Hence, the main objective of this study is to utilize Bootstrap method to construct a 100(1-α)% confidence interval for the difference between two non-normal process capability indices, CNpk1 -CNpk2. The proposed Bootstrap interval can be effectively employed to determine which one of the two production processes or manufacturers has a better production capability. Moreover, engineers without much statistics background can easily adopt the proposed index and related procedures when comparing processes or selecting an alternative supplier.

中文摘要…………………………………………………………………I
英文摘要………………………………………………………………II
誌謝……………………………………………………………………III
目錄……………………………………………………………………IV
圖目錄…………………………………………………………………V
表目錄……………………………………………………………VI
第一章 緒論………………………………………………………1
1.1 研究背景與動機…………………………………………1
1.2 研究目的…………………………………………………3
1.3 研究範圍…………………………………………………3
1.4 研究架構…………………………………………………4
第二章 文獻探討 ……………………………………5
2.1 製程能力指標介紹………………………………………5
2.2 非常態製程能力指標介紹………………………………6
2.3 複式模擬法………………………………………………10
2.4 其他相關文獻探討………………………………………13
第三章 研究方法……………………………………………15
3.1 複式信賴區間建構流程…………………………………15
3.1.1 有效性分析………………………………………………17
3.1.2 敏感度分析………………………………………………18
3.1 應用流程………………………………………………37
第四章 實例說明……………………………………39
第五章 結論………………………………………………………41
參考文獻……………………………………………………………42

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