A distribution-free robust method for monitoring linear profiles using rank-based regression

Profile monitoring is a technique for checking the stability of the functional relationship between a response variable and one or more explanatory variables over time. Linear profile monitoring is particularly useful in practice due to its simplicity and flexibility. The existing monitoring methods suffer from a drawback in that they all assume the error distribution to be normal. When the underlying distribution is misspecified, the efficiency of the commonly used Least Squares Estimation (LSE) is likely to be low and as a consequence the detection ability of procedures based on LSE is reduced. To overcome this drawback, this article develops a non-parametric methodology for monitoring the linear profile, including the regression coefficients and profile variations. The Multivariate Sign Exponentially Weighted Moving Average (MSEWMA) control scheme is applied to the estimated profile parameters obtained using a rank-based regression approach. Benefiting from certain favorable properties of MSEWMA and the efficiency of rank-based regression estimators, the proposed chart is robust from the point of view of the in-control and out-of-control average run length, particularly when the process distribution is heavily tailed. An example with real data from a manufacturing facility shows that it performs well in application.