A Generalized Linear Statistical Model Approach to Monitor Profiles

Abstract

Statistical process control methods for monitoring processes with univariate ormultivariate measurements are used widely when the quality variables fit to known probabilitydistributions. Some processes, however, are better characterized by a profile or a function of qualityvariables. For each profile, it is assumed that a collection of data on the response variable along withthe values of the corresponding quality variables is measured. While the linear function is thesimplest, it occurs frequently that many of the nonlinear functions may be transferred to linearfunctions easily. This paper proposes a control chart based on the generalized linear test (GLT) tomonitor coefficients of the linear profiles and an R-chart to monitor the error variance, thecombination of which is called GLT/R chart. While fixed values of the explanatory variables arecornerstones in other control charts proposed to monitor profiles, in GLT/R chart, it is not a necessarycondition. In order to illustrate the robustness of the GLT/R chart a simulation study has been done intwo different cases, i.e. fixed and non-fixed values of the explanatory variables. Then, the resultsobtained from GLT/R charts are compared to the ones from a multivariate T2 and ExponentiallyWeighted Moving Average/R (EWMA/R) control charts.