近年來，製程能力指標(Process Capability Index)已經非常廣泛地應用於品質管理上。製程能力指標用來表示製造過程中所產出產品的能力的優劣，在實際應用上，仍以傳統上的Cp與Cpk指標最為常用。但此些指標仍有一些缺失處，尤其是在不對稱規最為明顯。本文以偏移量與容差(tolerance)之比產生的懲罰比率來修正常見的指標Cp與Cpk，因此提出了六個新指標。文內探討這些新指標的估計式及其統計性質，並因此修正估計式找出偏量與均方差較小的估計方法。結果顯示無論在對稱規格或不對稱規格下，新指標的表現比較不會傾向極端且能反映出真實的製程能力。

　　In recent, Process Capability Index (PCI) has already used in the quality management extensively. The value of PCI can use to decide the capability of the production fit in with the process specifications. In real world, the most popular indices are Cp and Cpk. But these indices still have some defects, especially in asymmetrical specifications. We take a penalty ratio from the ratio of the shift to tolerance to modify the Cp index and Cpk index. We therefore bring up six new indices. The estimators of the new indices and their statistical properties are discussed. We find that the naive estimator can be modified such that the new estimator has smaller bias and MSE. It shows the performances of the new indices don’t tend to extreme and can reflect the real process capability under the symmetrical or asymmetrical specification.

【1】Boyles, R. A. (1994), “Process Capability with Asymmetric Tolerances”,
Communications in Statistics-Computation and Simulation 23(3), pp. 615-643.

【2】Chan, L. K., Cheng, S. W. and Spiring, F. A. (1988), “A New Measure of Process Capability：Cpm”, Journal of Quality Technology 20, pp. 162-175.

【3】Chen, K. S., Pearn, W. L. and Lin, P. C. (1999), “A New Generalization of Cpm for Process with Asymmetric Tolerances”, International Journal of Reliability Quality and Safety Engineering 6(4), pp. 383-398.

【4】Juran, J. M. (1974), Quality Control Handbook, 3rd ed, McGraw-Hill, New York.

【5】Kane, V. E. (1986), “Process Capability Indices”, Journal of Quality Technology 18, pp. 41-52.

【6】Kotz, S. and Johnson, N. L. (1993), Process Capability Indices, Chapman & Hall, New York.

【7】Kolarik, W. J. (1995), Creating quality:/concepts, systems, strategies, and tools, McGraw-Hill, New York

【8】Pearn, W. L., Kotz, S. and Johnson, N. L. (1992), “Distributional and Inferential Properties of Process Capability Indices”. Journal of Quality Technology 24, pp. 216-233.

【9】Vännman, K. (1995), “A Unified Approach to Capability Indices”, Statistica Sinica 5, pp. 805-820.

【10】Vännman, K. (1997), “A General Class of Capability Indices in the Case of Asymmetric Tolerances”, Communications in Statistics-Theory and Methods 26(8), pp. 2049-2072.

【11】余少方 (2000)，在規格非對稱下一個新的製程能力指標，國立成功大學統計學研究所碩士論文

【12】李士康 (2001)，使用渴望函數的非對稱製程能力指標，國立成功大學統計學研究所碩士論文

【13】潘浙楠、李文瑞 (2003)，品質管理，俊傑書局股份有限公司