Drift time detection and adjustment procedures for processes subject to linear trend

摘要

This paper considers production processes when the mean of a quality characteristic is drifted linearly with time. First, it introduces a procedure to detect the drift time of the process mean as early as possible. Then, based on the estimate of the drift time, a new adjustment procedure based on the maximum likelihood estimate of the drift time is developed to keep the process mean on target. The paper analyses and compares the performance of the proposed estimator with cumulative sum (CUSUM) and exponentially moving average (EWMA) change point estimation procedures. It is observed that the proposed procedure indeed estimates the drift time effectively for moderate and large trend rates. However, there is a noticeable decrease in its ability to detect drift time at small trend rates. Furthermore, the performance of the new adjustment procedure is compared with EWMA controllers. It is shown that the new procedure is more stable through a wide range of trend rates and its performance does not depend on any parameters of the process.