Abstract

Profile monitoring is a technique for monitoring the stability of a functional relationship between a response variable and one or more explanatory variables over time. General linear profiles monitoring is the most important one because the relationship between the response variable and the explanatory variables is easy to characterize by linearity besides its flexibility and simplicity. In addition, most of general linear profiles monitoring techniques assume normality of error random variables. However, the normality of error random 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 nonparametric charting scheme for Phase II monitoring of general linear profiles where normality of error random variables is not assumed. The proposed charting method applies the cumulative sum (CUSUM) to the Pearson chi-square test of the vector of the Wilcoxon-type rank-based estimators of regression coefficients and an error variance estimator. Performance properties of the developed control chart are evaluated and compared with existing charting methods in terms of average run length (ARL). A real example is also used to illustrate the applicability and implementation of the proposed monitoring scheme.