臺灣博碩士論文加值系統

製程能力指標廣泛的應用在製造業上，由於這些指標精確地量化製程能力與製程表現，因此這些指標對於成功的改善製程品質與製程流程上，扮演重要的角色。然而，在大多數的製程能力分析上卻未考慮量測誤差，在衡量製程能力時，描述品質特徵的資料卻是與量測工具息息相關的，因此，若不考慮量測誤差下，只依照單一的製程能力指標值來衡量製程能力的結論將是不可靠的。在我們的研究中，我們討論量測誤差對於製程能力指標Cp、Cpk、Cpu和Cpl的估計值有哪些影響，並且提出修正的信賴區間與檢定臨界值，以應用於量測誤差在不可避免下的製程能力分析。我們的研究可以幫助實行者做精確的製程能力評估，並做較可靠的決策。

Process capability indices have been widely used in the manufacturing industry. Those capability indices, quantifying process potential and performance, are important for any successful quality improvement activities and quality program implementation. Most research works related to process capability analysis have assumed no gauge measurement errors. However, the quality of data on the process characteristics relies very much on the gauge measurement. Conclusions about capability of the process just only based on the single numerical value of the index are not reliable. In our research study, we conduct the performance of the estimators of the indices, Cp, Cpk, Cpu and Cpl with gauge measurement errors, and present adjusted confidence interval bounds and critical values for capability estimation or testing purpose of those indices with unavoidable measurement errors. Our research would help practitioners to determine whether the factory processes meet the capability requirement, and make more reliable decisions.

Abstract (Chinese) ………………………………i
Abstract ………………………………………....ii
List of Contents …………………………..…iii
Chapter 1. Introduction ……………… ……….1
Chapter 2. Process Precision Measure with Presence of Gauge Measurement Errors………..........……………………...7
Chapter 3. Measuring Process Capability Based on with Gauge Measurement Errors …………………………………..20
Chapter 4. One-sided Process Capability Assessment in the Presence of Gauge Measurement Errors ……………………….32
Chapter 5. Conclusions ………………………………………….44
References ……………………………………………….…….….45
Appendix ………………………… ……………………………....49

[1] Bordignon, S. and Scagliarini, M. (2002). Statistical analysis of process capability indices with measurement errors. Quality and Reliability Engineering International, 18, 321-332.
[2] Boyles, R. A. (1991). The Taguchi capability index. Journal of Quality Technology, 23(3), 615-643.
[3] Burdick, R. K. and Larsen, G. A. (1997). Confidence intervals on measures of variability in R&R Studies. Journal of Quality Technology, 29(3), 261-273.
[4] Chan, L. K., Cheng, S. W. and Spiring, F. A. (1988). A new measure of process capability: Cpm . Journal of Quality Technology, 20(3), 162-175.
[5] Chan, L. K., Xiong, Z. and Zhang, D. (1990). On the asymptotic distributions of some process capability indices. Communication in Statistics-Theory and Methods, 19(1), 11-18.
[6] Chou, Y. M. and Owen, D. B. (1989). On the distributions of the estimated process capability indices. Communication in Statistics-Theory and Methods, 18, 4549-4560.
[7] Chou, Y. M., Owen, D. B. and Borrego, A. S. (1990). Lower confidence limits on process capability indices. Journal of Quality Technology 22, 223-229.
[8] Dolezal, K. K., Burdick, R. K. and Birth N. J. (1998). Analysis of a two-factor R&R Study with fixed operators. Journal of Quality Technology, 30(2), 163-170.
[9] Finley J. C. (1992). What is capability ? Or what is Cp and Cpk. ASQC Quality Congress Transactions, Nashville, 186-191.
[10] Floyd, D. A. and Laurent, C. J. (1995). Gauging: an underestimated consideration in the application of statistical process control. Quality Engineering, 8(1), 13-29.
[11] Franklin, L.A. and Wasserman, G. S. (1991). Bootstrap confidence interval estimates of Cpk: an introduction. Communications in Statistics: Simulations and Computation, 20, 231-242
[12] Franklin, L. A. and Wasserman G. S. (1992). Bootstrap lower confidence limits for capability indices. Journal of Quality Technology, 24(4), 196-210.
[13] Hamada, M. and Weerahandi, S. (2000). Measurement system assessment via generalized inference. Journal of Quality Technology, 32(3), 241-253.
[14] Hoffman, L. L. (2001). Obtaining confidence intervals for Cpk using percentiles of the distribution of Cp. Quality and Reliability Engineering International, 17(2), 113-118.
[15] Juran, J. M., Gryna, F. M. and Bingham, R. S. Jr. (1974). Quality Control Handbook. McGraw-Hill, New York.
[16] Kane, V. E. (1986). Process capability indices. Journal of Quality Technology, 18(1), 41-52.
[17] Kocherlakota, S. (1992). Process capability index: recent development. Sankya: The Indian Journal of Statistics, 54(B), Pt. 3, 352-369.
[18] Kotz, S. and Johnson, N. L. (1993). Process Capability Indices, Chapman & Hall, London.
[19] Kotz, S., and Lovelace, C. (1998). Process capability indices in theory and practice. Arnold, London, U.K.
[20] Kotz, S., Pearn, W. L. and Johnson, N. L. (1993). Some process capability indices are more reliable than one might think. Journal of the Royal Statistical Society, Series C, 42(1), 55-62.
[21] Kushler, R. and Hurley, P. (1992). Confidence bounds for capability indices. Journal of Quality Technology, 24, 188-195.
[22] Levinson, W. A. (1995). How good is your gage?. Semiconductor International, 165-168.
[23] Levinson, W. A. (1996). Do you need a new gage?. Semiconductor International, 113-117.
[24] Li, H., Owen, D. B. and Borrego, S. A. (1990). Lower confidence limits on process capability indices based on the range. Communication in Statistics- Simulation and Computation, 19(1), 1-24.
[25] Lin, P. C. and Pearn, W. L. (2002). Testing process capability for one-sided specification limit with application to the voltage level translator. Microelectronics Reliability, 42(12), 1975-1983.
[26] Mandel, J. (1972). Repeatability and reproducibility. Journal of Quality Technology, 4(2), 74-85.
[27] Mittag, H. J. (1997). Measurement error effects on the performance of process capability indices. Frontiers in Statistical Quality Control, 5, 195-206.
[28] Mizuno, S. (1988). Company-wide Total Quality Control, Asian Productively Organization, Tokyo.
[29] Montgomery, D. C. and Runger, G. C. (1993). Gauge capability and designed experiments. Part I: basic methods. Quality Engineering, 6(1), 115-135.
[30] Montgomery, D. C. and Runger, G. C. (1993). Gauge capability analysis and designed experiments. Part II: experimental design models and variance component estimation. Quality Engineering, 6(2), 289-305.
[31] Montgomery, D. C. (2000). Introduction to Statistical Quality Control, 4th Edition, John Wiley and Sons, New York.
[32] Nagata, Y. and Nagahata, H. (1994). Approximation formulas for the lower confidence limits of process capability indices. Okayama Economic Review, 25, 301-314.
[33] Pearn, W. L. and Chen, K. S. (1999). Making decisions in assessing process capability index Cpk. Quality and Reliability Engineering International, 15, 321-326.
[34] Pearn, W. L., Chen, K. S. and Lin, P. C. (1999). The probability density function of the estimated process capability index Cpk. Far East Journal of Theoretical Statistics, 3(1), 67-80.
[35] Pearn, W. L. and Chen, K. S. (2002). One-sided capability indices Cpu and Cpl: decision making with sample information. International Journal of Quality & Reliability Management, 19(3), 221-245.
[36] Pearn, W. L., Lin, G. H. and Chen, K. S. (1998). Distributional and inferential properties of the process accuracy and process precision indices. Communications in Statistics-Theory and Methods, 27(4), 985-1000.
[37] Pearn, W. L. and Lin, P. C. (2002). Testing process performance based on the capability index Cpk with critical values. Computers and Industrial Engineering, 47, 351-369 .
[38] Pearn, W. L., Kotz, S. and Johnson, N. L. (1992). Distributional and inferential properties of process capability indices. Journal of Quality Technology, 24, 216-231.
[39] Pearn W. L. and Shu, M. H. (2003). Manufacturing capability control for multiple power distribution switch processes based on modified Cpk MPPAC. Microelectronics Reliability, 43, 963-975.
[40] Pearn, W. L. and Sue, M. H. (2003). An algorithm for calculating the lower confidence bounds of Cpl and Cpu with application to low-drop-out linear regulators. Microelectronics Reliability, 43, 495-502.
[41] Rocke, D. M. and Lorenzato, S. (1995). A two-component model for measurement error in analytical chemistry. Technometrics, 37(2), 176-184.
[42] Spiring, F. A., Leung, B., Cheng, S. and Yeung, A. (2003). A bibliography of process capability papers. Quality and Reliability Engineering International, 19, 1-16.
[43] Tang, L. C., Than, S. E. and Ang, B. W. (1997). A graphical approach to obtaining confidence limits of Cpk. Quality and Reliability Engineering International, 13, 337-346.
[44] Vännman, K. (1995). A unified approach to capability indices. Statistica Sinica, 5, 805-820.
[45] Vännman, K. and Kotz, S. (1995). A superstructure of capability indices distributional properties and implications. Scandinavian Journal of Statistics, 22, 477-491.
[46] Vännman, K. (1997). Distribution and moments in simplified form for a general class of capability indices. Communications in Statistics: Theory and Methods, 26, 159-179.
[47] Vardeman, S. B. and Vanvalkenburg, E. S. (1999). Two-way random-effects analyses and gauge R&R studies. Technometrics, 41(3), 202-211.
[48] Wang, C. M. and Iyer, H. K. (1994). Tolerance intervals for the distribution of true values in the presence of measurement errors. Technometrics, 36(2), 162-170.
[49] Wilson, A., Hamada, M., and Xu, M. (2004). Assessing production quality with nonstandard measurement errors. Journal of Quality Technology, 36(2), 193-206.
[50] Zhang, N. F., Stenback, G. A. and Wardrop, D. M. (1990). Interval estimation of process capability index . Communications in Statistics: Theory and Methods, 19, 4455-4470.