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Abstract:
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In recent years, the study of the effects of parameters estimation on the performance and design of control charts has been predominantly focused on the conditional perspective, which is based on the run length distribution conditioned on the parameter estimates and the Exceedance Probability Criterion. That is, for the case of two-sided variance control charts, this perspective is equivalently based on the tolerance interval (TI) for the sample variance distribution, specifically, on the traditional TI that controls the center of this distribution. However, since this type of TI could cause the specified proportion of the sample variance distribution to lie concentrated at one tail, this design criterion could lead to detecting alarms due to the corresponding charting statistics are out of only one of the two control limits. With this motivation, we propose a new design criterion of two-sided variance control charts with estimated parameters based on another type of TI that controls both tail proportions of the sample variance distribution. The results related to the proposed design are compared with those of the traditional chart design, highlighting its relevant advantages.
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