Cluster-Based Profile Analysis in Phase I

Our proposed technique, referred to as cluster-based profile monitoring, incorporates a cluster-analysis phase to aid in determining the possible existence of profiles in the historical data set resulting from an out-of-control process. The proposed method first replaces the data from each sampled unit with an estimated profile, using some appropriate regression method, and clusters the profiles based on their estimated parameter vectors. This yields an initial main cluster, which contains at least half the profiles. The initial estimated parameters for the population average (PA) profile are obtained by fitting a linear mixed model to those profiles in the main cluster. Profiles that are not contained in the initial main cluster may be iteratively added to the main cluster and the mixed model used to update the estimated parameters for the PA profile. Those profiles contained in the final main cluster are considered as resulting from the in-control process while those not included are considered as resulting from an out-of-control process. A simulated example, a Monte Carlo study, and an application demonstrate the performance advantages of this proposed method over a non-cluster based method with respect to more accurate estimates of the PA parameters and improved classification performance criteria. When the profiles can be represented by m ρ × 1 vectors, the profile monitoring process is equivalent to the detection of multivariate outliers. For this reason, we also compare our proposed method to a popular method used to identify outliers when dealing with a multivariate response. Our study demonstrates that, when the out-of-control process corresponds to a sustained shift, the cluster-based method using the successive difference estimator is clearly the superior method, among those methods we considered, based on all performance criteria.