A method of estimating the process capability index from the first four moments of non-normal data

Quality and Reliability Engineering International

Volumn 20, Issue 8, 2004, Pages 787-805

  Ding, Jianmin ^a  

^a AGERE SYSTEMS   (United States)

Author keywords

Chebyshev Hermite polynomials; Effective range; Non normal data; Process capability index

Indexed keywords

ALGEBRA; ALGORITHMS; FUNCTIONS; LEAST SQUARES APPROXIMATIONS; PROBABILITY DENSITY FUNCTION; SAMPLING;

CHEBYSHEV-HERMITE POLYNOMIALS; EFFECTIVE RANGE; NON-NORMAL DATA; PROCESS CAPABILITY INDEX;

STATISTICAL PROCESS CONTROL;

EID: 11044237513     PISSN: 07488017     EISSN: None     Source Type: Journal    
DOI: 10.1002/qre.610     Document Type: Article

References (40)

1. Kotz S, Johnson NL. Process capability indices - a review, 1992-2000. Journal of Quality Technology 2002; 34:2-19.
2. Bothe DR. Measuring Process Capability. McGraw-Hill: New York, 1997.
3. Kotz S, Lovelace CR. Process Capability Indices in Theory and Practice. Arnold: London, 1998.
4. Sze SM. VLSI Technology (2nd edn). McGraw-Hill: New York, 1988; 332-340.
5. Nielson LS. The calculation of process capability indices. Journal of Quality Technology 1999; 31:249-250.
6. Ryan T. Discussion on 'Controversies and contradictions in statistical process control'. Journal of Quality Technology 2000; 32:367-369.
7. Gunter BH. The use and abuse of Cpk: Part 3. Quality Progress 1989; 5:79-80.
8. Somerville SE, Montgomery DC. Process indices and non-normal distributions. Quality Engineering 1996-97; 9:305-316.
9. Clements JA. Process capability calculations for non-normal distributions. Quality Progress 1989; 22(2):95-100.
10. Pearn WL, Kotz S. Application of Clements' method for calculating second and third generation process capability indices for non-normal Pearsonian populations. Quality Progress 1994; 7(1): 139-145.
11. Bittanti S, Lovera M, Moiraghi L. Application of non-normal process capability indices to semiconductor quality control. IEEE Transactions on Semiconductor Manufacturing 1998; 11(2):296-303.
12. Polansky AM. A smooth nonparametric approach to process capability. Quality and Reliability Engineering International 1998; 14:43-48.
13. Polansky AM. An algorithm for computing non-parametric capability estimate. Journal of Quality Technology 2000; 32:284-289.
14. Page M. Analysis of non-normal process distributions. Semiconductor International 1994; 17:88-96.
15. Farnum NR. Using Johnson curves to describe non-normal data. Quality Engineering 1996-97; 9:329-336.
16. Chou YM, Polansky AM, Mason RL. Transforming non-normal data to normality in statistical process control. Journal of Quality Technology 1998; 30:133-141.
17. Polansky AM, Chou YM, Mason RL. An algorithm for fitting Johnson transformations to non-normal data. Journal of Quality Technology 1999; 31:345-350.
18. Box GEP, Cox DR. An analysis of transformations. Journal of the Royal Statistical Society Series B 1964; 26:221-252.
19. Breyfogle FW. Implementing Six Sigma. Wiley: New York, 1999.
20. Lu M-W, Rudy RJ. Discussion on 'Process capability indices - a review, 1992-2000'. Journal of Quality Technology 2002; 34:38-39.
21. Choi IS, Bai DS. Process capability indices for skewed populations. Proceeding of 20th International Conference on Computers and Industrial Engineering. ICC & IE: Kyongju, Korea, 1996; 1211-1214.
22. Wu H-H, Swain J. A Monte Carlo comparison of capability indices when processes are non-normally distributed. Quality and Reliability Engineering International 2001; 17:219-231.
23. Wright PA. A process capability index sensitive to skewness. Journal of Statistical Computation and Simulation 1995; 52:195-203.
24. Chang YS, Bai DS. Control charts for positively-skewed populations with weighted standard deviations. Quality and Reliability Engineering International 2001; 17:397-406.
25. Chang YS, Bai DS. Process capability indices for skewed populations. Quality and Reliability Engineering International 2002; 18:383.
26. Nahar PC, Hubele NF, Zimmer LS. Assessment of a capability index to skewness. Quality and Reliability Engineering International 2001; 17:233-241.
27. Tang LC, Than SE. Computing process capability indices for non-normal data: A review and comparative study. Quality and Reliability Engineering International 1999; 15:340-353.
28. Borges WS, Ho LL. A fraction defective based capability index. Quality and Reliability Engineering International 2001:17:447-458.
29. Bordignon S, Scagliarini M. Statitical analysis of process capability indices with measurement errors. Quality and Reliability Engineering International 2002; 18:321-332.
30. Pearn WL, Chen KS. Making decisions in assessing process capability index Cpk. Quality and Reliability Engineering International 1999; 15:321-326.
31. Pearn WL, Chem KS. One-sided capability indices Cpu and Cpl: Decision making with sample information. Quality and Reliability Engineering International 2002; 19:221-245.
32. Pearn WL, Lin PC. Computer program for calculating the p-value in testing process capability index Cpmk. Quality and Reliability Engineering International 2002; 18:333-342.
33. p. Quality and Reliability Engineering International 2001; 17:113-118.
34. Zimmer LS, Hubele NF, Zimmer WJ. Confidence intervals and sample size determination for Cpm. Quality and Reliability Engineering International 2001; 17:51-68.
35. Shiau JJH, Chang CT, Hung HN. A Bayesian procedure for process capability assessment. Quality and Reliability Engineering International 1999; 15:369-378.
36. Deleryd M, Vännman K. Process capability plots - a quality improvement tool. Quality and Reliability Engineering International 1999; 15:213-227.
37. Hamaker HC. Relative merits of using maximum error versus 3σ in describing the performance of laser-exposure reticle writing systems. Optical/Laser Microlithography VIII (Proceedings of SPIE, vol. 2440), Brumer TA (eds.). SPIE: Bellingham, WA, 1995; 550-559.
38. Hamaker HC. Improved estimates of the range of errors on photomask using measured values of skewness and kurtosis. 15th Annual Symposium on Photomask Technology and Management (Proceedings of SPIE, vol. 2621), Sheldon GV, Wiley JN (eds.). SPIE: Bellingham, WA, 1995; 198-207.
39. Kendall MG, Stuart A. The Advanced Theory of Statistics Volume 1 Distribution Theory. Macmillan: New York, 1977.
40. Hill ID, Hill R, Holder RL. Fitting Johnson curves by moments. Applied Statistics 1976; 25:180-184.