Profile monitoring is becoming popular in the area of quality control. It is used when the process is characterized by the relationship between a response variable and some explanatory variables at each time period. This paper considers the situation where profiles are modeled parametrically using a multiple linear regression with random errors following an autoregressive moving-average process. Diagnostic schemes to find out-of-control samples are developed for this purpose. A simulation study examines the performance of the proposed approach based on the average run length criterion. Lastly, a real example illustrates the results, after considering both Phase I and Phase II schemes.