Abstract
Control charts based on regression models are appropriate for monitoring in which the quality characteristics of products vary depending on the behavior of predecessor variables. Its use enables monitoring the correlation structure between input variables and the response variable through residuals from the fitted model according to historical process data. However, such strategy is restricted to data from input variables which are not significantly correlated. Otherwise, colinear variables that hold substantial information on the variability of the response variable might be absent in the regression model adjustment. This paper proposes a strategy for monitoring count data combining Poisson regression and principal component analysis. In such strategy, colinear variables are turned into uncorrelated variables by principal component analysis and a Poisson regression is performed on principal component scores. A deviance residual control chart from the fitted model is then used to evaluate the process. The performance of that new approach is illustrated through a case study in a plastic plywood process with real and simulated data.
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References
Mandel BJ (1969) The regression control charts. J Qual Technol 1:1–9
Zhang GX (1985) Cause-selecting control charts—a new type of quality control charts. QR J 12:221–225
Hawkins DM (1993) Regression adjustment for variables in multivariate quality control. J Qual Technol 25:170–182
Haworth DA (1996) Regression control charts to manage software maintenance. Softw Maint Res Pract 8:35–48
Wade MR, Woodall WH (1993) A review and analysis of cause-selecting control charts. J Qual Technol 25:161–169
Shu L, Tsui K, Tsung F (2008) A review of regression control charts. Encycl Statist Qual Reliab 260:1–9
Asadzadeh S, Aghaie A, Shahriari H (2009) Monitoring dependent process steps using robust cause-selecting control charts. Qual Reab Eng Int 25:851–874
Skinner KR, Montgomery DC, Runger GC (2003) Process monitoring for multiple count data using generalized linear model-based control charts. Int J Prod Res 41:1167–1180
Skinner KR, Montgomery DC, Runger GC (2004) Generalized-linear model-based control charts for discrete semiconductor process data. Qual Reliab Eng Int 20(8):777–786
Jearkpaporn D, Montgomery DC, Runger GC, Borror CM (2003) Process monitoring for correlated gamma-distributed data using generalized linear model-based control charts. Qual Reliab Eng Int 19:477–491
Jearkpaporn D, Montgomery DC, Runger GC, Borror CM (2005) Model-based process monitoring using robust generalized linear models. Int J Prod Res 43(7):1337–1354
Kang L, Albin SL (2000) On-line monitoring when the process yields a linear profile. J Qual Technol 32:418–426
Kim K, Mahmoud MA, Woodall WH (2003) On the monitoring of linear profiles. J Qual Technol 35:317–328
Mahmoud MA, Woodall WH (2004) Phase I analysis of linear profiles with calibration applications. Technometrics 46:380–391
Mahmoud MA, Parker PA, Woodall WH, Hawkins DM (2007) A change point method for linear profile data. Qual Reliab Eng Int 23:247–268
Noorossana R, Vaghefi SA, Dorri M (2011) Effect of non-normality on the monitoring of simple linear profiles. Qual Reliab Eng Int 27:425–436
Ayoubi M, Kazemzadeh RB, Noorossana R (2014) Estimating multivariate linear profiles change point with a monotonic change in the mean of response variable. Int J Adv Technol 75:1537–1556
Amiri A, Koosha M, Azhdari A, Wang G (2015) Phase I monitoring of generalized linear model-based regression profiles. J Stat Comput Simul 85:2839–2859
Nomikos P, Macgregor JF (1995) Multivariate SPC charts for monitoring batch processes. Technometrics 37:41–59
McCullagh P, Nelder JA (1989) Generalized linear models, 2ªth edn. Chapman & Hall, London
Myers RH, Montgomery DC, Vining GG (2002) Generalized linear models with applications in engineering and the sciences. John Wiley & Sons, New York
Jackson JE (1991) A user’s guide to principal components. John Wiley & Sons, New York
Jackson JE, Mudholkar GS (1979) Control procedures for residuals associated with principal component analysis. Technometrics 21(3):341–349
Rencher AC (2002) Methods of multivariate analysis, 2ªth edn. John Wiley & Sons, New York
Rajab JM, MatJafri MZ, Lim HS (2013) Combining multiple regression and principal component analysis for accurate predictions for column ozone in Peninsular Malaysia. Atmos Environ 71:36–43
Sayadi AR, Lashgari A, Paraszczak J (2012) Hard-rock LHD cost estimation using single and multiple regressions based on principal component analysis. Tunn Undergr Space Technol 27:133–141
Jolliffe IT (2004) Principal component analysis, 2ªth edn. Springer, New York
Neter J, Kutner MH, Nachtsheim CJ, Li W (2005) Applied linear statistical models, 5th edn. McGraw-Hill/Irwin, New York
Demirkir C, Özsahin S, Aydin I, Colakoglu G (2013) Optimization of some panel manufacturing parameters for the best bonding strength of plywood. Int J Adhes Adhes 46:14–20
Fang L, Chang L, Guo W-J, Chen Y, Wang Z (2014) Influence of silane surface modification of veneer on interfacial adhesion of wood–plastic plywood. Appl Surf Sci 288:682–689
Azaman MD, Sapuan SM, Sulaiman S, Zainudin ES, Khalina A (2013) Shrinkages and warpage in the processability of wood-filled polypropylene composite thin-walled parts formed by injection molding. Mater Des 52:1018–1026
R Development Core Team. (2014). R: a language and environment for statistical computing. R Foundation for Statistical Computing, ISBN 3-900051-07-0, 2014. Available at http://www.r-project.org.
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Marcondes Filho, D., Sant’Anna, A.M.O. Principal component regression-based control charts for monitoring count data. Int J Adv Manuf Technol 85, 1565–1574 (2016). https://doi.org/10.1007/s00170-015-8054-6
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DOI: https://doi.org/10.1007/s00170-015-8054-6