Adaptive memory control charts constructed on generalized likelihood ratio test to monitor process location

Abstract

An adaptive cumulative sum (CUSUM) control chart based on the classical exponential weighted moving average (EWMA) statistic and Huber’s function, symbolized as an ACUSUM E control chart, is an enhanced form of the classical CUSUM control chart that can identify different sizes of shift. However, the classical EWMA statistic for the ACUSUM E control chart does not provide explicit rule for parameter choices to diagnose a specific shift. To overcome this issue, this study has proposed two ACUSUM control charts, symbolized as ACUSUM c control charts to monitor a specific and a certain range of shift. The novelty behind the proposed ACUSUM c (ACUSUMc(1) and ACUSUMc(2)) control charts is initially adaptively updating the reference parameter using the classical CUSUM statistic, generalized likelihood ratio test, and score functions to achieve superior performance. An algorithm in MATLAB using the Monte Carlo simulation technique is designed to obtain numerical results. Furthermore, based on numerical results, performance evaluation measures such as average run length, extra quadratic loss, relative average run length, and comparison index are calculated. The proposed ACUSUM C control charts based on performance evaluation measures and visual presentation are compared against other control charts. Findings reveal the superiority of the proposed ACUSUM C control charts. Besides, for practical point of view, the proposed ACUSUMC(1) control chart is implemented with numerical data to show the significance over other control charts.