A new non-parametric control chart for monitoring general linear profiles based on log-linear modelling

Profile monitoring has received much attention from the applications in statistical process control. It is a method for monitoring the stability of a functional relationship between a response variable and one or more explanatory variables over the time axis. General linear profiles monitoring is very important since the linear relationship between a response variable and explanatory variables is easy to characterize besides it is simple and flexible. In addition, most of general linear profiles monitoring techniques assume normality of random error variables. However, the normality of random error variables is not satisfied in certain applications. This causes the existing monitoring methods for general linear profiles both inadequate and inefficient. Based on the log-linear modelling, in this paper, we develop a non-parametric control chart for Phase II monitoring of general linear profiles where normality of random error variables is not assumed. The proposed charting method applies the CUSUM (cumulative sum) to the Pearson chi-square test for the Wilcoxon-type rank-based estimators of coefficient parameters and an estimator of random error variance. Effectiveness of the developed control chart is assessed and compared with that of two existing control charts based on the criterion of ARL (average run length). An industrial production process example is also applied to illustrate how the proposed control chart can be used in practice.