Growing Profile Monitoring with Dynamic Time Warping Alignment

In conventional profile monitoring problems, profiles for different products or process runs are assumed to have the same length. Statistical monitoring cannot be implemented until the whole profiles are obtained. However, in some cases, a profile should be monitored when it growth with time, so that the root causes can be identified and automatic compensations can be initiated as early as possible. Motivated by an ingot growth process in semiconductor manufacturing, we propose a monitoring method for growing profiles with unequal lengths and time-varying means. The profiles are firstly aligned by using dynamic time warping (DTW) algorithm, and then averaged to generate a baseline. Online monitoring is performed based on the incomplete growing profiles. Both simulation studies and a real example are used to demonstrate the performance of the proposed method.