Alternative Shewhart-type charts for grouped observations

摘要

Classical Shewhart control charts based on groups of observations use the average as statistic to decide whether a signal should be produced or not. Assuming a known process distribution here several other statistics are investigated as well. Moreover, individual charts are compared with charts with larger group size. The chart using the minimum of each group of observations is a promising new proposal. The behavior of the minimum-chart is competitive to that of the average-chart when distributions are known. Moreover, when the process distribution is unknown, for this chart (nonparametric) estimation of an extreme quantile is reduced to estimation of an ordinary quantile of the underlying distribution itself, which is far easier to perform accurately.