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