Variables control chart limits and tests for special causes

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Abstract
Control charts are used to detect problems in control such as outliers, shifts in levels or excess variability in subgroup means that may have a special cause. This paper addresses itself to deriving control chart limits based on past data and based on initial samples in a current control situation. We present a general setting for control charts. Furthermore, an overview is given of tests for special causes. The tests are standardized so that the asymptotic type I error does not exceed a fixed level. The distributions of the run lengths of the tests and combinations of tests are also evaluated. We propose to use a low percen‐tile of the run length distribution, instead of the average run length, to study the performance of the tests. These indicate that, in particular when tests are combined, the run length percentiles may be too small for practical purposes. It is shown that (nearly) exact control chart limits for observations from a normal distribution exist. The traditional limits differ considerably from the proposed ones and correspond to even smaller run length percentiles.

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