A Phase I Cluster‐Based Method for Analyzing Nonparametric Profiles

Abstract

A cluster‐based method has been used successfully to analyze parametric profiles in Phase I of the profile monitoring process. Performance advantages have been demonstrated when using a cluster‐based method of analyzing parametric profiles over a non‐cluster based method with respect to more accurate estimates of the parameters and improved classification performance criteria. However, it is known that, in many cases, profiles can be better represented using a nonparametric method. In this study, we use the cluster‐based method to analyze profiles that cannot be easily represented by a parametric function. The similarity matrix used during the clustering phase is based on the fits of the individual profiles with p‐spline regression. The clustering phase will determine an initial main cluster set that contains greater than half of the total profiles in the historical data set. The profiles with in‐control T2 statistics are sequentially added to the initial main cluster set, and upon completion of the algorithm, the profiles in the main cluster set are classified as the in‐control profiles and the profiles not in the main cluster set are classified as out‐of‐control profiles. A Monte Carlo study demonstrates that the cluster‐based method results in superior performance over a non‐cluster based method with respect to better classification and higher power in detecting out‐of‐control profiles. Also, our Monte Carlo study shows that the cluster‐based method has better performance than a non‐cluster based method whether the model is correctly specified or not. We illustrate the use of our method with data from the automotive industry. Copyright © 2014 John Wiley & Sons, Ltd.