The Comparison between the Trimmed Mean CUSUM Chart and the Standard Mean CUSUM Chart

This paper is concerned with the assessment of the performance of a robust Cumulative Sum (CUSUM) chart, which is called the Trimmed CUSUM Chart. A standard CUSUM chart is based on standard mean whilst the robust CUSUM chart is based on the trimmed mean. A series of simulations have been carried out to compare the performance of trimmed mean and standard mean CUSUM procedures by looking at the values of the average run length (ARL) and the ratio between the ARL with a mean shift and ARL without. The results show that for normal process and a sample size of 5, the standard mean CUSUM performs better than the trimmed mean CUSUM, but their performances are equally well as sample size is increased. However, for data with one outlier and highly skewed process, which is sample are simulated from a Student T and Chi Square distributions with 4, 6 and 7 degree of freedom (suitably shifted and scaled to produce common mean and variance, i.e. m = 0 and s2 = 1), the trimmed mean seems to perform better than the standard mean CUSUM.