A spatial rank-based EWMA chart for monitoring linear profiles

Profile monitoring has been recently considered as one of the most promising areas of research in statistical process monitoring (SPM). It is a technique for monitoring the stability of a functional relationship between a dependent variable and one or more independent variables over time. The monitoring of linear profiles is the most popular one because the relationship between the dependent variable and the independent variables is easy to describe by linearity, in addition to its flexibility and simplicity. Furthermore, almost all existing charting schemes for monitoring linear profiles assume that error terms are normally distributed. In some applications, however, the normality assumption of error terms is not justified. This makes the existing charting schemes not only inappropriate but also less efficient for monitoring linear profiles. In this article, based on the spatial rank-based regression, we propose a charting method for monitoring linear profiles where the error terms are not normally distributed. The charting scheme applies the exponentially weighted moving average (EWMA) to the spatial rank of the vector of the Wilcoxon-type rank-based estimators of regression coefficients and a transformed error variance estimator. Performance properties of the proposed charting scheme are evaluated and compared with an existing charting method based on multivariate sign in terms of the in-control (IC) and out-of-control (OC) average run length (ARL). Finally, a real example is used to demonstrate the applicability and implementation of the proposed charting scheme.