Phase II Multiple Linear Regression Profile with Small Sample Sizes

In some statistical process control applications, the quality of a process or product is best represented by a functional relationship between a response variable and one or more explanatory variables. Different methods have been proposed in the literature to monitor phase II multiple linear regression profile. Most of the existing approaches assume the number of sample observations to be greater than the number of explanatory variables, a condition needed to estimate the model parameters and establish chart statistics. In practice, however, the sample size can be smaller than the number of the multiple linear regression parameters. None of the previous studies of multiple regression profiles approaches have tackled this problem. In the current study, two methods are proposed to handle the problem of profile monitoring with sample sizes smaller than the number of regression parameters. Simulation results show that both methods outperform the existing methods in the literature used to monitor multiple linear regression profile. Moreover, both methods work satisfactorily when existing methods cannot be applied, that is, when the sample size is smaller than the number of profile parameters.