Unaligned Profile Monitoring Using Penalized Methods

In some manufacturing processes, complex profiles are collected to characterize quality status. However, some of these profiles may have unequal lengths, which makes the attempt of directly comparing them difficult. In addition, when a shift occurs in a profile, it usually affects a segment of continuously connected observations. That is, local shifts instead of global shifts are frequently seen. As shift signals are easily mixed with allowable mean trends, statistical monitoring of such unaligned profiles becomes a challenging task. In this paper, we propose a framework for monitoring profiles with unequal lengths. The profiles are first aligned using a modified robust dynamic time warping (DTW) algorithm, which is insensitive to local mean shifts. Penalization-based methods are then used to estimate profile means. Finally, mean estimates are utilized in a likelihood ratio test statistic for effective monitoring. Both simulation studies and a real example are used to demonstrate the effectiveness of the proposed monitoring procedure.