An adaptive CUSUM chart for drift detection

• Published in: Quality and reliability engineering international Vol. 38; no. 2; pp. 887 - 894
• Main Authors: Yi, Fan, Qiu, Peihua
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 01.03.2022
• Subjects: adaptive CUSUM chart; CUSUM charts; Drift; drift detection; exponentially weighted least square; Likelihood ratio; linear drift; Process controls; Statistical analysis; Statistical process control
• ISSN: 0748-8017; 1099-1638
• DOI: 10.1002/qre.3020

In practice, sequential processes often have gradual changes in their process distributions over time. This is related to the drift detection problem in statistical process control. In the literature, there have been some existing discussions on this problem. But, most existing methods are designed based on the assumption that the related drift is linear or have another specific pattern. In reality, however, such specified patterns may not be valid. In this paper, we suggest an adaptive cumulative sum (CUSUM) chart to handle the drift detection problem with a flexible drift pattern. The new method integrates the general framework to construct a CUSUM chart based on the generalized likelihood ratio statistic and estimation of a shift size by the exponentially weighted least square regression procedure. Simulation studies show that the proposed method is effective in various cases considered. The new method is also illustrated using an example about the exchange rates between Indian Rupees and US Dollars.