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Abstract:
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Statistical process control (SPC) and monitoring techniques are often used in applications where multiple sources of variation are present, as for example in a variance components model. Control charts are useful in these situations and have been considered in some earlier works by Roes and Does (1995), Woodall and Thomas (1995) and others in the literature. We present refinements and adaptations of these charts based on the knowledge gained and the advancements made over the last several years on retrospective and prospective process monitoring. This work takes proper account of the effects of parameter estimation while designing and implementing the control charts. In the sequel, we calculate the corrected (adjusted) control limits in both Phase I and Phase II applications, two important phases of the overall SPC regime. In Phase I, the correct control limits are obtained using a multivariate t (normal) distribution. In Phase II, two types of corrected limits are provided, following the recent literature, one based on the unconditional perspective and the other based on the conditional perspective and the exceedance probability criterion (EPC). Results, tabulations and illustrations with data make the methodologies employable in practice. An R package is provided to help deployment of the new methodology.
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