On the monitoring of simple linear Berkson profiles

Quality and Reliability Engineering International

Volumn 28, Issue 8, 2012, Pages 949-965

  Wang, Yi Hua Tina ^a   Huwang, Longcheen ^a  

^a NATIONAL TSING HUA UNIVERSITY   (Taiwan)

Author keywords

average run length; change point; control chart; EWMA; generalized likelihood ratio

Indexed keywords

AVERAGE RUN LENGTHS; CHANGE-POINTS; CONTROL CHARTS; EWMA; GENERALIZED LIKELIHOOD RATIO;

QUALITY ASSURANCE; SAFETY ENGINEERING;

SEMICONDUCTOR DEVICE MANUFACTURE;

EID: 84870248832     PISSN: 07488017     EISSN: 10991638     Source Type: Journal    
DOI: 10.1002/qre.1286     Document Type: Article

References (54)

1. Woodall WH, Spitzner DJ, Montgomery DC, Gupta S,. Using control charts to monitor process and product quality profiles. Journal of Quality Technology 2004; 36: 309-320.
2. Kang L, Albin SL,. On-line monitoring when the process yields a linear profile. Journal of Quality Technology 2000; 32: 418-426.
3. Kim K, Mahmoud MA, Woodall WH,. On the monitoring of linear profiles. Journal of Quality Technology 2003; 35: 317-328.
4. Gupta S, Montgomery DC, Woodall WH,. Performance evaluation of two methods for online monitoring of linear calibration profiles. International Journal of Production Research 2006; 44: 1927-1942.
5. Croarkin C, Varner R., Measurement assurance for dimensional measurements on integrated-circuit photomasks. NBS Technical Note 1164, U.S. Department of Commerce, 1982.
6. Mahmoud MA, Woodall WH,. Phase I monitoring of linear profiles with calibration application. Technometrics 2004; 46: 380-391.
7. Zou C, Zhang Y, Wang Z,. Control chart based on change-point model for monitoring linear profiles. IIE Transactions 2006; 38: 1093-1103.
8. Mahmoud MA, Parker PA, Woodall WH, Hawkins DM,. A change point method for linear profile data. Quality and Reliability Engineering International 2007; 23: 247-268.
9. Zou C, Zhou C, Wang X, Tsung F,. A self-starting control chart for linear profiles. Journal of Quality Technology 2007; 39: 364-375.
10. Zou C, Tsung F, Wang Z,. Monitoring general linear profiles using multivariate exponentially weighted moving average schemes. Technometrics 2007; 49: 395-408.
11. Jesen DR, Hui YV, Ghare PM,. Monitoring an input-output model for production. I: The control charts. Management Science 1984; 30: 1197-1206.
12. Mestek O, Pavlik J, Suchanek M,. Multivariate control charts: Control charts for calibration curves. Journal of Analytical Chemistry 1994; 350: 344-351.
13. Stover FS, Brill RV,. Statistical quality control applied to ionchromatography calibrations. Journal of Chromatography. A 1998; 804: 37-43.
14. Lawless JF, Mackay RJ, Robinson JA,. Analysis of variation transmission in manufacturing process, part I. Journal of Quality Technology 1999; 31: 131-142.
15. Walker E, Wright S,. Comparing curves using additive models. Journal of Quality Technology 2002; 34: 118-129.
16. Williams JD, Woodall WH, Birch JB,. Statistical monitoring of nonlinear product and process quality profiles. Quality and Reliability Engineering International 2007; 23: 925-941.
17. Colosimo BM, Pacella M,. On the use of principal component analysis to identify systematic patterns in roundness profiles. Quality and Reliability Engineering International 2007; 23: 707-725.
18. Williams JD, Birch JB, Woodall WH, Ferry NM,. Statistical monitoring of heteroscedastic dose-response profiles from high-throughput screening. Journal of Agricultural, Biological, and Environmental Statistics 2007; 12: 216-235.
19. Jin J, Shi J,. Feature-preserving data compression of stamping tonnage information using wavelet. Technometrics 1999; 41: 327-339.
20. Lada EK, Lu J-C, Wilson JR,. A wavelet-based procedure for process fault detection. IEEE Transactions on Semiconductor Manufacturing 2002; 15: 79-90.
21. Ding Y, Zeng L, Zhou S,. Phase I analysis for monitoring nonlinear profiles in manufacturing processes. Journal of Quality Technology 2006; 38: 199-216.
22. Zou C, Tsung F, Wang Z,. Monitoring profiles based on nonparametric regression methods. Technometrics 2008; 50: 512-526.
23. Fan J, Zhang C, Zhang J,. Generalized likelihood ratio statistics and Wilks phenomenon. The Annals of Statistics 2001; 29: 153-193.
24. Fan J, Gijbels I,. Local Polynomial Modeling and Its Applications. Chapman & Hall: London, 1996.
25. Qiu P, Zou C, Wang Z,. Nonparametric profile monitoring by mixed effects modeling. Technometrics 2010; 52: 265-293.
26. Berkson J,. Are there two regressions? Journal of the American Statistical Association 1950; 45: 164-180.
27. Rosner B, Willett WC, Spiegelman D,. Correction of logistic regression relative risk estimates and confidence intervals for systematic within-person measurement error. Statistics in Medicine 1989; 8: 1051-1069.
28. Rosner B, Spiegelman D, Willett WC,. Correction of logistic regression relative risk estimates and confidence intervals for measurement error: The case of multiple covariates measured with error. American Journal of Epidemiology 1990; 132: 734-745.
29. Tosteson TD, Stefanski LA, Schafer DW,. A measurement error model for binary and ordinal regression. Statistics in Medicine 1989; 8: 1139-1147.
30. Schafer DW, Gilbert ES,. Some statistical implications of dose uncertainty in radiation dose-response analyses. Radiation Research 2006; 166: 303-312.
31. Quesenberry CP,. On properties of Q charts for variables. Journal of Quality Technology 1995; 27: 184-203.
32. Chen G, Cheng SW, Xie H,. Monitoring process mean and variability with one EWMA chart. Journal of Quality Technology 2001; 33: 223-233.
33. Lowry CA, Woodall WH, Champ CW, Rigdon SE,. A multivariate exponentially weighted moving average control chart. Technometrics 1992; 34: 46-53.
34. Huwang L, Wang YT, Yeh AB, Chen, ZJ,. On the exponentially weighted moving variance. Naval Research Logistics 2009; 56: 659-668.
35. Box GEP,. Some theorems on quadratic forms applied in the study of analysis of variance problems: Effect on inequality of variance in one-way classification. Annals of Mathematical Statistics 1954; 25: 290-302.
36. Lawless JF,. Statistical Models and Methods for Lifetime Data (2nd edn). Wiley: New York, 2003.
37. Shu L, Jiang WA,. new EWMA chart for monitoring process dispersion. Journal of Quality Technology 2008; 40: 319-331.
38. Acosta-Mejia CA,. Monitoring process dispersion. Ph.D. Dissertation, Texas A&M University, College Station, Texas, 1995.
39. Acosta-Mejia CA, Pignatiello JJ Jr,. Monitoring Process Dispersion without Subgrouping. Journal of Quality Technology 2000; 32: 89-102.
40. Hawkins DM, Qiu P, Kang CW,. The changepoint model for statistical process control. Journal of Quality Technology 2003; 35: 355-366.
41. Hawkins DM, Zamba KD,. Statistical process control for shifts in mean or variance using a change-point formulation. Technometrics 2005; 47: 164-173.
42. Hawkins DM, Zamba KD,. A change-point model for a shift in variance. Journal of Quality Technology 2005; 37: 21-31.
43. Pignatiello JJ, JR, Samuel TR. Estimation of the change point of a normal process mean in SPC applications. Journal of Quality Technology 2001; 33: 82-95.
44. Andrews DWK,. Testing for parameter instability and structural change with unknown change point. Econometrica 1993; 61: 821-856.
45. Bai J,. Estimation of a change point in multiple regression models. The Review of Economics and Statistics 1997; 79: 551-563.
46. Csörgo M, Horváth L,. Limit theorems in change-point analysis. Wiley Series in Probability and Statistics, Wiley: New York, 1997.
47. Liu J, Wu S, Zidek JV,. On segmented multivariate regressions. Statistica Sinica 1997; 7: 497-525.
48. Bai J,. Likelihood ratio tests for multiple structural changes. Journal of Econometrics 1999; 91: 299-323.
49. Bai J, Perron P,. Estimating and testing linear models with multiple structural changes. Econometrica 1998; 66: 47-78.
50. Bai J, Perron P,. Critical values for multiple structural change tests. The Econometrics Journal 2003; 6: 72-78.
51. Qu Z, Perron P,. Estimating and testing structural changes in multivariate regressions. Econometrica 2007; 75: 459-502.
52. Wang YT,. On the monitoring of linear Berkson profiles. Ph.D. Dissertation, National Tsing Hua University, Hsinchu, Taiwan, 2010.
53. Reynolds MR, JR, Stoumbos ZG. Should exponentially weighted moving average and cumulative sum charts be used with Shewhart limits? Technometrics 2005; 47: 409-424.
54. Montgomery DC,. Introduction to Statistical Quality Control (6th edn). Wiley: New York, 2009.