傳統上工業界透過管制圖與直方圖進行長期與短期製程能力分析，藉以了解關鍵品質特性的表現。當發現製程表現不佳時，便著手進行品質改善，而改善的成效除了藉由Cp，Cpk等製程能力指標反映改善前後的結果外，工程師們亦應該透過成本/損失的估計，凸顯品質問題的嚴重性，使高階主管能重視品質改善的迫切性而予以全力支持。因此透過成本損失的觀念來探討製程能力指標所代表之意義再進行製程改善，將更能反映製程改善的成效。
本研究係歸納在單邊規格與雙邊規格對稱及非對稱情形下，製程能力指標Cp、Cpk及Cpm與田口二次損失、INLF及RINLF等損失函數之期望損失公式，使從事品管的人員對製程能力指標與期望損失能有方便估算的方式。至於關鍵品質特性則考慮服從四種常見分配：（1）常態分配；（2）均等分配；（3）指數分配及（4）對數常態分配。另外，我們針對產品品質特性服從常態分配時，推導出製程能力指標與期望損失之關係式，並將常態分配下製程能力指標值所對應之不良率與期望損失製成對照表，以方便業界查詢。

Traditionally, engineers analyze the long-term and short-term process capabilities by using control charts and the histograms to understand the performances of key characteristics. When the process doesn’t perform well, quality improvement actions will be taken. The process capability indices, such as Cp and Cpk, can reflect the results of improvement. In addition, engineers should also estimate costs / losses in order to highlight the seriousness of the quality problem, so that the senior management will pay attention to the urgency of quality improvement and render their support. By associating process capability indices with quality losses, the results of process improvement can be reflected in a better way.
This research systematically summarizes the process capability indices：Cp, Cpk and Cpm, and the associated formulae of loss functions：Taguchi Loss Function, INLF and RINLF, for both unilateral and the bilateral specifications under the following four distributions：（1）Normal（2）Uniform（3）Exponential（4）Lognormal. It will provide quality practitioners an easier way to calculate the process capability indices and expected losses. Moreover, the relationships between process capability indices and expected losses for normal distribution has been successfully derived. Based on the above formulae of relationships, a summary table that lists various process capability indices and their corresponding nonconforming rates and expected losses has also been established. It can serve as a convenient reference for quality practitioners.

【1】 Chan, L. K., Cheng, S. W. and Spiring, F. A., “A New Measure of Process Capability, Cpm,” Journal of Quality Technology, 20, pp.160-175 (1988).
【2】 Clements, John A., “Process Capability Calculations for Non-Normal Distributions,” Quality Progress, 22, pp.95-100 (1989).
【3】 Gunter, B., “The Use and Abuse of Cpk：Part 1,” Quality Progress, pp.72-73 (1989).
【4】 Gunter, B., “The Use and Abuse of Cpk：Part 2,” Quality Progress, pp.108-109 (1989).
【5】 Gunter, B., “The Use and Abuse of Cpk：Part 3,” Quality Progress, pp.79-80 (1989).
【6】 Gunter, B., “The Use and Abuse of Cpk：Part 4,” Quality Progress, pp.86-87 (1989).
【7】 Johnson, R. A. and Wichern, D. W., Applied Multivariate Statistical Analysis, 4th edition, Prentice-Hall International, Inc. (1998).
【8】 Johnson, T., “The Relationship of Cpm to Squared Error Loss,” Journal of Quality Technology, 24, pp.211-215 (1992).
【9】 Juran, J. M., Quality Control Handbook, 3rd edition, McGraw-Hill, New York (1974).
【10】 Kane, V. E., “Process Capability indices,” Journal of Quality Technology, 18, pp.41-52 (1986).
【11】 Leon, R. V. and Wu, C. F., “A Theory of performance Measures in Parameter Design,” Statistica Sinica, 2, pp.335-358 (1992).
【12】 Pan, J. N. and Wang, J. H., “A Study of Loss Functions for Product Interference Analysis,” Industrial Engineering Research, 2(1), pp.80-100 (2000).
【13】 Pearn, W. L., Kotz, S. and Johnson, N. L., “Distribution and Inferential Properties of Process Capability Indices,” Journal of Quality Technology, 24, pp.216-231 (1992).
【14】 Rodriguez, R. N., “Recent Developments in Process Capability Analysis,” Journal of Quality Technology, 24, pp.176-187 (1992).
【15】 Spiring, F. A., “The Reflected Normal Loss Function,” The Canadian Journal of Statistics, 21, pp.321-330 (1993).
【16】 Spiring, F. A. and Yeung, A. S., “A General Class of Loss Functions with Industrial Applications”, Journal of Quality Technology, 30, pp.152-162 (1998).
【17】 Taguchi, G., Introduction to Quality Engineering: Designing Quality Into Products and Processes, Asian Productivity Organization, Tokyo (1986).
【18】 潘浙楠 及 李文瑞, 品質管理, 華泰書局,(2002).
【19】 潘浙楠 及 李育宗, “單邊規格下產品損失函數之研究,” 品質學報
第八卷 第一期 pp.39-66 (2002).
【20】 潘浙楠 及 吳淑鈴, “非常態資料製程能力指標之研究,” 品質學報
第二卷 第二期 pp.77-95 (1996).