The Max-CUSUM Chart

Abstract

Control charts have been widely used in industries to monitor process quality. We usually use two control charts to monitor the process. One chart is used for monitoring process mean and another for monitoring process variability, when dealing with variables data. A single Cumulative Sum (CUSUM) control chart capable of detecting changes in both mean and standard deviation, referred to as the Max-CUSUM chart is proposed. This chart is based on standardizing the sample means and standard deviations. This chart uses only one plotting variable to monitor both parameters. The proposed chart is compared with other recently developed single charts. Comparisons are based on the average run lengths. The Max-CUSUM chart detects small shifts in the mean and standard deviation quicker than the Max-EWMA chart and the Max chart. This makes the Max-CUSUM chart more applicable in modern production process where high quality goods are produced with very low fraction of nonconforming products and there is high demand for good quality.

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