修正型損失函數在制定經濟工程規格上之應用研究

Applying Revised Loss Function in the Economic Tolerance Design

潘浙楠(Jen-Nan Pan) ； 李婉瑜(W. Y. Lee)

《品質學報》 13卷3期 (2006/09) Pp. 241-256

摘要

傳統上工業界認為產品品質特性之量測值只有在超出規格界限時才會造成報廢或重作之損失。自從田口提出以二次損失函數的概念作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使用。然而在工業產品之生產過程中，工程規格之制定與損失函數之選取方式均可能影響品質成本的估算。一般而言，工程規格可分為望目、望小與望大特性三類。為了使工程規格之制定符合實際情況，本研究針對Kapur經濟模式進行修正並考慮產品品質特性呈常態分配。至於損失函數方面則考慮(1)田口二次　(2)INLF (3)RINLF三種以估算顧客及生產者所遭受之期望損失（報廢、重作及檢驗成本等），期能制定出使單位產品之平均總期望損失最小的經濟工程規格。此外，我們亦推導出產品品質特性服從常態分配下，製程能力指標與單位產品期望損失之關係式，並利用此一對應之關係式選擇適當的損失函數，研究結果顯示修正型損失函數(RINLF)較田口二次損失與Spiring的INLF損失函數更能反映產品不良率的期望損失及製程的改善狀況。
最後，本研究利用一組電路板焊接之實際資料，以RINLF修正型損失函數進行最佳經濟工程規格之制定。研究之成果可做為相關業界在制定經濟工程規格及監控製程品質上的重要參考。

關鍵字

經濟工程規格 ； 田口二次損失函數 ； 修正型損失函數

並列摘要

Engineering tolerance design plays an important role in modern manufacturing and assembly processes of industrial products. Generally speaking, quality characteristics can be divided into three types: nominal the best, larger the better and smaller the better. Since the quadratic loss function proposed by Taguchi, the quality loss concept has been shifted from ”defined by specification limits” to ”defined by user”.
In order to minimize total quality costs due to variation, inspection, and costs associated with nonconforming units (scrap or rework), we modify the Kapur's model and then establish economic specification limits for both symmetric and asymmetric cases. Three different loss functions (1) Taguchi's quadratic loss function (2) Inverted Normal Loss Function, INLF (3) Revised Inverted Normal Loss Function, RINLF have been considered in this research. Moreover, the relationships between process capability indices and expected loss per unit under normal distribution have been successfully derived. Based on the above formulae of relationships, we have show that RINLF is the most appropriate loss function to establish economic specification limits since it can better describe the actual loss of a process.
Finally, a realistic QFP data from a solder paste stencil printing process was used to demonstrate the economic tolerance setting using RINLF. The results suggest that the revised inverted normal loss function be used in determination of economic specification limits.

並列關鍵字

economic tolerance design ； Taguchi's quadratic loss function ； inverted normal loss function INLF ； revised inverted normal loss function RINLF

參考文獻

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