Profile Monitoring of Residual Control Charts under Gamma Additive Models
Keywords:Average run length, EWMA control charts, gamma additive residuals, generalized additive models
One of the most powerful tools in quality control is the statistical control chart. In some process control applications, the quality of a product or process can be characterized by a relationship between two or more variables, which is typically referred to as a profile. There are many techniques in literature for monitoring profiles. Generalized additive models (GMAs) have been used frequently in many different applications for modeling non-linear effects in regression models with non-Gaussian response Hastie and Tibshirani (1987). The scheme is based on the deviance residuals, and Pearson residuals for detecting any disturbance in the control variables. This paper investigates the performance of exponentially weighted moving average (EWMA) control charts to monitor the response variability for gamma additive regression models. The simulation study shows that using deviance residuals under log link function seems more suitable than Pearson residuals.
Areepong Y. Comparison of performance of residual control charts for trend stationary AR (p) processes. Int J Pure Appl Math. 2013; 85(3): 583-592.
Braimah OJ, Osanaiye PA, Omaku PE, Saheed YK, Eshimokhai SA. On the use of exponentially weighted moving average (Ewma) control chart in monitoring road traffic crashes. Int J Math Stat Invent. 2014; 2(5): 1-9.
Cordeiro GM, Simas AB. The distribution of Pearson residuals in generalized linear models. Comput Stat Data Anal. 2009; 53(9): 3397-3411.
Cuerv EC, Corrales M, Cifuentes MV, Zarate H. On gamma regression residuals. J Iran Stat Soc 2016; 15(1): 29-44.
Gipe GW. Using residual analysis to search for specification errors. Decis Sci. 1976; 7(1): 40-56.
Hastie T, Tibshirani R. Generalized additive models: some applications. J Am Stat Assoc. 1987; 82(398): 371-386.
Hastie TJ, Tibshirani RJ. Generalized additive models. Chapman and Hall/CRC; 1990.
Hunter JS. The exponentially weighted moving average. J Qual Technol. 1986; 18(4): 203-210.
Khan N, Yasmin T, Aslam M, Jun CH. On the performance of modified EWMA charts using resampling schemes. Oper Res Decis. 2018; 28(3): 29-43.
Knoth S. Accurate ARL calculation for EWMA control charts monitoring normal mean and variance simultaneously. Sequential Anal. 2007; 26(3): 251-263.
Lu CW, Reynolds Jr MR. EWMA control charts for monitoring the mean of autocorrelated processes. J Qual Technol. 1999; 31(2): 166-188.
Lucas JM, Saccucci MS. Exponentially weighted moving average control schemes: properties and enhancements. Technometrics. 1990; 32(1): 1-12.
Mahmoud MA. Simple linear profiles. In Noorossana R, Saghaei A, Amiri A (Eds.). Statistical Analysis of Profile Monitoring (ed., pp. 21-92). John Wiley & Sons; 2011.
Mahmoud MA. The performance of phase II simple linear profile approaches when parameters are estimated. Commun Stat Simul 2012; 41(10): 1816-1833.
Maravelakis PE, Castagliola P, Khoo MBC. Run length properties of run rules EWMA chart using integral equations. Qual Technol Quant Manag. 2019; 16(2): 129-139.
McCullagh P, Nelder JA. Generalized linear models. Chapman and Hall/CRC; 1989.
Messaoud A, Theis W, Hering F, Weihs C. Monitoring a drilling process using residual control charts. Qual Eng. 2008; 21(1): 1-9.
Pierce DA, Schafer DW. Residuals in generalized linear models. J Am Stat Assoc. 1986; 81(396): 977-986.
Pregibon D. Logistic regression diagnostics. Ann Statist. 1981; 9(4): 705-724.
Roberts SW. Control chart tests based on geometric moving averages. Technometrics. 1959; 239-250.
Shao YE, Lin Y. Applying residual control charts to identify the false alarms in a TFT-LCD manufacturing process. Appl Math Inf Sci. 2013; 7(4):1459-1464.
Swartzman G, Silverman E, Williamson N. Relating trends in Walleye Pollock (Theragra chalcogramma) abundance in the Bering Sea to environmental factors. Can J Fish Aquat Sci. 1995; 52(2): 369-380.
Woodall WH, Spitzner DJ, Montgomery DC, Gupta S. Using control charts to monitor process and product quality profiles. J Qual Technol. 2004; 36(3): 309-320.
Yee TW, Mitchell ND. Generalized additive models in plant ecology. J Veg Sci. 1991; 2(5): 587-602.
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