Summary: This article considers the Phase I analysis of data when the quality of a process or product is characterized by a multiple linear regression model. This is usually referred to as the analysis of linear profiles in the statistical quality control literature. The literature includes several approaches for the analysis of simple linear regression profiles. Little work, however, has been done in the analysis of multiple linear regression profiles.
This article proposes a new approach for the analysis of Phase I multiple linear regression profiles. Using this approach, regardless of the number of explanatory variables used to describe it, the profile response is monitored using only three parameters, an intercept, a slope, and a variance. Using simulations, the performance of the proposed method is compared to that of the existing methods for monitoring multiple linear profile data in terms of the probability of a signal. The advantage of the proposed method over the existing methods is the greatly improved detection of changes in the process parameters of linear profiles in high-dimensional spaces. The article also proposes useful diagnostic aids based on \(F\)-statistics to help in identifying the source of profile variation and the locations of out-of-control samples. Finally, the use of multiple linear profile methods is illustrated by a data set from a calibration application at the National Aeronautics and Space Administration (NASA) Langley Research Center.