On the Monitoring of Linear Profiles

AbstractWe propose control chart methods for process monitoring when the quality of a process or product is characterized by a linear function. In the historical analysis of Phase I data, we recommend methods including the use of a bivariate T2 chart to check for stability of the regression coefficients in conjunction with a univariate Shewhart chart to check for stability of the variation about the regression line. We recommend the use of three univariate control charts in Phase II. These three charts are used to monitor the 𝘠-intercept, the slope, and the variance of the deviations about the regression line, respectively. A simulation study shows that this type of Phase II method can detect sustained shifts in the parameters better than competing methods in terms of average run length performance. We also relate the monitoring of linear profiles to the control charting of regression-adjusted variables and other methods.KeywordsCalibrationExponentially Weighted Moving Average Control ChartMultivariate T2 Control ChartsStatistical Process Control Additional informationNotes on contributorsKeunpyo KimMr. Kim is a Ph.D. student in the Department of Statistics. His email address is kekim@vt.edu.Mahmoud A. MahmoudMr. Mahmoud is a Ph.D. student in the Department of Statistics. His email address is mamahmou@vt.edu.William H. WoodallDr. Woodall is a Professor in the Department of Statistics. He is a Fellow of ASQ. His email address is bwoodall@vt.edu.