THE MEDIAN ABSOLUTE DEVIATIONS AND THEIR APPLICATIONS TO SHEWHART CONTROL CHARTS

Abstract

Standard Shewhart control charts with estimated control limits are widely used in practice. There are four ways to estimate the standard deviation σ generally, as which we call the average range, the average sample standard deviation, the pooled sample standard deviation and the average absolute deviation, respectively. We give three new estimators which are based on median in order to estimate standard deviation in this paper, and we get their means through simulated computation. The simulated results are then used to discuss their properties when the data is from a ϵ-contaminated normal distribution. At last, we simulate the in-control and out-of-control average run lengths of Shewhart control charts when the process standard deviation is estimated by seven different ways including three absolute deviations to median mentioned in the paper.

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