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系統識別號 U0026-0407201222495000
論文名稱(中文) 望目及望小特性下,非常態多變量製程能力指標之制定與評估
論文名稱(英文) Development of Non-Normal Multivariate Process Capability Indices for Nominal-the-Best and Smaller-the-Better Cases
校院名稱 成功大學
系所名稱(中) 統計學系碩博士班
系所名稱(英) Department of Statistics
學年度 100
學期 2
出版年 101
研究生(中文) 石維謙
研究生(英文) Wei-Cheng Shih
學號 r26994044
學位類別 碩士
語文別 中文
論文頁數 62頁
口試委員 指導教授-潘浙楠
口試委員-鄭春生
口試委員-溫敏杰
口試委員-鄭順林
中文關鍵字 多變量製程能力指標  望目特性  望小特性 
英文關鍵字 Multivariate process capability indices  nominal-the-best cases  smaller-the-better cases 
學科別分類
中文摘要 一般而言,工業製程中常有多個彼此相關的品質特性皆可能造成產品與製程異常。目前已有多位學者致力於多重品質特性(多變量)製程能力指標之研究,但彼等之研究多著重在品質特性呈常態之情況。實務上,一些與環境績效或與能源使用有關的多重關鍵品質特性卻常呈現非常態分配且為相依資料的情況,然而,甚少學者探討此類狀況下多變量製程能力指標之制定。因此,本研究擬探討當多重品質特性呈非常態分配且產品工程規格屬望目及望小特性情形下非常態多變量製程能力指標之制定與評估,我們利用Weighted Standard Deviation (WSD)方法對Pan與Lee (2010) 所訂定之常態多變量製程能力指標NMCp與NMCpm指標進行修正,並據此制定出新的非常態多變量製程能力指標RNMCp(Revised NMCp)和RNMCpm(Revised NMCpm)。此外,針對Niverthi與Dey (1995) 訂定望小特性下的多變量常態製程能力指標(ND index),我們亦利用WSD法進行修正並提出改良的非常態多變量製程能力指標RNMCpu。
最後,我們以模擬的方式比較於不同右(左)偏分配組合下,本研究所提出之新指標與MCp、MCpm、NMCp、NMCpm及ND在反映非常態多變量製程表現上之優劣。模擬分析結果顯示無論製程平均是否偏離目標值,新非常態多變量製程能力指標與上述指標相較均能正確反映非常態多變量製程真實的不良率。
英文摘要 Generally, an industrial product has more than one quality characteristic. In order to establish performance measures for evaluating the capability of a multivariate manufacturing process, several multivariate process capability indices have been developed based on the assumption of normality in the past few years. However, the environmental performance, such as air pollution and energy utilization data may not follow normal distribution. Thus, in this research, we develop two non-normal multivariate process capability indices; RNMCp (Revised NMCp) and RNMCpm (Revised NMCpm) by relieving the normality assumption for both nominal-the-best and smaller-the-better cases. Based on the two normal multivariate process capability indices proposed by Pan and Lee (2010), we use weighted standard deviation method (WSD) to revise their NMCp and NMCpm indices. In addition, we also use WSD method to revise a multivariate process capability index (ND index) established by Niverthi and Dey (1995).
Finally, we conduct simulation studies to compare the performance of correctly reflecting the true nonconforming rate among these multivariate indices. Simulation results show that our proposed indices outperform MCp, MCpm, NMCp, NMCpm and ND indices under different combinations of two right skewed/left skewed distributions regardless of the process mean hitting the target or not.
論文目次 第一章 緒論 1
1.1 研究背景與動機 1
1.2 研究目的 2
1.3 研究架構 2
第二章 文獻回顧與探討 4
2.1 單變量(單一品質特性)製程能力指標 4
2.1.1 單變量常態製程能力指標 4
2.1.2 Krishnamoorthi的單一變量製程能力指標 5
2.2 多變量(多重品質特性)製程能力指標 6
2.2.1 Kocherlakota et al.的雙變量製程能力指標(KK) 6
2.2.2 Niverthi與Dey的雙變量製程能力指標(ND) 6
2.2.3 多變量製程能力指標MCp與MCpm 7
2.2.4 多變量製程能力指標NMCp與NMCpm 8
2.3 WSD方法 10
2.3.1 單變量WSD 方法(Weighted Standard Deviation Method) 10
2.3.2 製程能力指標 及 14
第三章 新非常態多變量製程能力指標 15
3.1 多變量WSD法(Multivariate Weighted Standard Deviation Method) 15
3.2 產品工程規格屬望目特性下,新非常態多變量製程能力指標之制定 19
3.3 產品工程規格屬望小特性下,新非常態多變量製程能力指標之制定 21
3.4 新非常態多變量製程能力指標之模擬 22
3.4.1 兩種比較準則之介紹 22
3.4.2 依準則1比較各多變量製程能力指標之優劣的模擬方法與結果 23
3.4.3 依準則2比較各多變量製程能力指標之優劣的模擬方法與結果 38
第四章 實例分析 43
第五章 結論與未來研究方向 46
5.1 結論 46
5.2 未來研究方向 47
參考文獻 48
附錄A 50
附錄B 61
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