Cluster-Based Profile Monitoring in Phase I Analysis

• Activity Number: 354
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Quality and Productivity Section
• Author(s): Yajuan Chen*+ and Jeffrey B. Birch and William H. Woodall
• Companies: Virginia Tech and Virginia Tech and Virginia Tech
• Keywords: Mixed Models ; Outliers ; Quality Control ; Robust Profile Monitoring ; T2 Statistic

Abstract

An innovative profile monitoring methodology is introduced for Phase I analysis. The 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. To cluster the profiles, 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 parameters. This cluster phase then 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, determined using the statistic, that are not contained in the initial main cluster are iteratively added to the main cluster and the mixed model is used to update the estimated parameters. The proposed method is demonstrated to have the performance advantage over a current non-cluster-based method with respect to more accurate estimates of the PA parameters.