Exceedance probabilities for parametric control charts
نویسندگان
چکیده
Common control charts assume normality and known parameters. Quite often these assumptions are not valid and large relative errors result in the usual performance characteristics, such as the false alarm rate or the average run length. A fully nonparametric approach can form an attractive alternative but requires more Phase I observations than are usually available. Sufficiently large parametric families then provide realistic intermediate models. In this paper the performance of charts based on such families is considered. Exceedance probabilities of the resulting stochastic performance characteristics during incontrol are studied. Corrections are derived to ensure that such probabilities stay within prescribed bounds. Attention is also devoted to the impact of the corrections for an outof-control process. Simulations are presented both for illustration and to demonstrate that the approximations obtained are sufficiently accurate for use in practice.
منابع مشابه
Are estimated control charts in control?
Standard control chart practice assumes normality and uses estimated parameters. Because of the extreme quantiles involved, large relative errors result. Here simple corrections are derived to bring such estimated charts under control. As a criterion, suitable exceedance probabilities are used.
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