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。

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.

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