Optimising the design of tabular mean CUSUM control chart to enhance the detection of diminutive process shifts

Abstract

Although the performance of the CUSUM chart in detecting small process shift is better than Shewhart chart, there exists cases in reality that require very quick response of detecting small process shift. This paper studies the influential factors that affect the CUSUM control chart design and its in-control and out-of-control average run length (ARL) values. The controllable factors studied are the slack value k; the decision interval h; and the Headstart or Fast Initial Response. These factors are varied at different values for the process expected shift (in standard deviation units) δ. Following this, a non-linear regression model is deduced to compute the ARL of the control chart at any combination of process and control chart variables. Optimisation model is utilised to achieve a specific value for the ARL through fixing the controllable factors. A computer program coded in Matlab workspace (Matlab and Statistics Toolbox Release, 2015) is used for the computation of the ARLs values.