科研之友
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摘要
Exponential weighted moving average and cumulative sum (CUSUM) control charts are well-known tool for their effectiveness in detecting small and moderate changes in the process parameters. To detect both large and small shifts, a new control structure is often recommended, named as combined Shewhart-CUSUM control chart, which combines the advantages of a Shewhart chart with the CUSUM chart. In this paper, we investigate 11 different standard deviation estimators with the structures of these 3 types of control charts for monitoring the process dispersion under normal and contaminated normal environments. By applying Monte Carlo simulations, we compare the performance of these memory charts depending on 4 factors: (1) standard deviation estimator, (2) parent environment, (3) chart type, and (4) change magnitude. Extensive simulations are used to compute and study the run length profiles of these memory charts, including the average, the standard deviation, the several percentiles, and the cumulative distribution function curves of the run length distribution. It turns out that there is a significant difference between the run length distribution of the memory chart with estimated parameters and the analogous case with known parameters, even using the adjusted control limits under normal environment, and the difference is more severe when contaminations are present. This difference is gradually diminished when a large number of Phase I samples is used under normality, but it is not true in the contaminated cases.
