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系統識別號 U0026-0812200915132338
論文名稱(中文) LINEX、INLF與RINLF損失函數在風險評估上之比較研究
論文名稱(英文) A Comparative Study of LINEX, INLF and RINLF Loss Functions on Risk Assessment
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 97
學期 2
出版年 98
研究生(中文) 盧為丞
研究生(英文) Wei-cheng Lu
學號 r2696106
學位類別 碩士
語文別 中文
論文頁數 86頁
口試委員 口試委員-鄭春生
口試委員-呂金河
指導教授-潘浙楠
中文關鍵字 製程能力指標  非對稱型損失函數  風險評估 
英文關鍵字 process capability indices  asymmetric loss function  risk assessment 
學科別分類
中文摘要 傳統上工業界常使用製程能力指標來評估關鍵產品品質特性的製程表現。自從田口提出二次損失函數的概念做為衡量產品品質損失的依據後,產品品質特性之量測值一旦偏離其目標值即可能產生損失之觀念遂逐漸為產學界所接受並廣泛地應用。透過成本/損失的估計,更能突顯產品品質問題之嚴重性,使高階主管能精確掌握及監控製程品質。製程之風險可視為產品之期望損失。因此藉由成本損失與製程能力指標的關聯來進行產品之量化風險評估,可同時評估製程失效的可能性及其影響,更能瞭解產品及製程之風險。
本研究考慮關鍵品質特性服從常態分配,在單邊規格與對稱型及非對稱型雙邊規格之情形下,探討並建立製程能力指標Cp、Cpk及Cpm與INLF、RINLF與RLINEX損失函數期望損失之關係式。以方便從事品管的人員在計算製程能力指標時,可同時估算其所對應的期望損失。研究結果顯示若產品未造成損失之區域已知且在目標值附近1/2倍容差內或更大時,以RINLF損失函數較能反映不良率之期望損失及製程風險;然而當產品未造成損失之區域為目標值附近0.18倍容差內甚至更小時,則以修正之RLINEX損失函數較能反映不良率之期望損失及製程風險。最後,我們將常態製程能力指標所對應之不良率與期望損失關係製成對照表,以方便使用者查詢。
英文摘要 Traditionally, engineers perform process capability indices to analyze the performance of key quality characteristics. Since the quadratic loss function proposed by Taguchi, the quality loss concept has been shifted from “defined by specification limits” to “defined by user”. Engineers should highlight the seriousness of the quality problem through cost/lost estimation, so the senior managers can handle and monitor the process quality precisely. The risk of process can be regarded as expected value of loss or an average loss. Therefore, practitioners can utilize the method of quantitative risk assessment linking the expected loss of failure and process capability indices to evaluate the likelihood and consequence of their processes.

The research establishes the relationship between various process capability indices, such as Cp, Cpk and Cpm, and three types of expected losses including INLF, RINLF and RLINEX under normal assumption for both unilateral and bilateral specifications. This approach gives decision-makers a concrete tool since the likelihood and consequence resulting from the failure of a manufacturing or environmental system can be evaluated simultaneously. The result suggest that if the acceptable range(in which no quality loss incurred) within the neighborhood of target value is 0.5 times or more of half of the specification width, RINLF is the most appropriate loss function in assessing manufacturing and environmental risks since it can better describe the actual loss of a process. If the acceptable range is below 0.18 times or smaller of half of the specification width, then RLINEX would be better.
Finally, several summary tables listing various process capability indices and their
expected losses as well as the corresponding failure rates have also been established.
Hopefully, the summary tables can provide a useful reference for quality practitioners in
conducting risk assessment.
論文目次 目 錄 I
圖目錄 III
表目錄 IV
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 3
第二章 相關文獻之回顧與探討 5
2.1 何謂品質損失 5
2.2 品質特性(Quality Characteristic)之分類 6
2.3 損失函數 7
2.3.1 傳統的損失函數 7
2.3.2 田口二次損失函數 8
2.3.3 轉換常態損失函數(Inverted Normal Loss Function, INLF) 10
2.3.4 修正轉換常態損失函數(Revised Inverted Normal Loss Function, RINLF) 12
2.3.5 LINEX損失函數(LINEX Loss Function) 14
2.4 常態製程能力指標 15
第三章 損失函數在風險分析上之比較 18
3.1 常態分配下期望損失之理論公式 18
3.1.1 雙邊規格(望目特性)下INLF期望損失之估算 18
3.1.2 雙邊規格(望目特性)下RINLF期望損失之估算 19
3.1.3 雙邊規格(望目特性)下LINEX期望損失之估算 19
3.2 修正LINEX損失函數 20
3.3 對稱型雙邊規格下期望損失與製程能力指標的關係 23
3.3.1 製程平均( )等於目標值( ) 23
3.3.2 製程平均( )小於目標值( ) 25
3.3.3 製程平均( )大於目標值( ) 28
3.4 非對稱型雙邊規格下期望損失與製程能力指標的關係 32
3.4.1 製程平均( )小於目標值( ) 32
3.4.2 製程平均( )大於目標值( ) 36
3.5 望小型(具目標值)單邊規格 39
3.6 損失函數之比較 41
第四章 數值實例分析與討論 48
4.1 建立正確單位產品風險之評估方式 48
4.2 數值實例分析:以IC封裝中QFP電路板焊接為例 49
第五章 結論與未來研究方向 52
5.1 結論 52
5.2 未來研究方向 53
參考文獻 54
附錄 A 56
附錄 B 69
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