SPC scheme to monitor linear predictors embedded in nonlinear profiles

摘要

Response Modeling Methodology (RMM) is a general platform to model monotone convex relationships. In this article, RMM is combined with linear regression analysis to model and estimate linear predictors (LPs) embedded in a nonlinear profile. A regression-adjusted statistical process control scheme is then implemented to monitor the LP's residuals. To model and estimate the LP, RMM defines a Taylor series expansion of an unknown response transformation and then use canonical correlation analysis to estimate the LP. A possible hindrance to the implementation of the new scheme is possible occurrence of nonnormal errors (in violation of the linear regression model). Reasons for the occurrence of this phenomenon are explored and remedies offered. The effectiveness of the new scheme is demonstrated for data generated via Monte Carlo simulation. Results from hypothesis testing clearly indicate that the type of the response distribution, its skewness and the sample size, do not affect the effectiveness of the new approach. A detailed implementation routine is expounded, accompanied by a numerical example. When interest is solely focused on the stability of the LP, and the nonlinear profile per se is of little interest, the new general RMM-based statistical process control scheme delivers an effective platform for process monitoring. Copyright (c) 2015 John Wiley & Sons, Ltd.