BMC Med Inform Decis Mak - Statistical process control for data without inherent order.


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CKGROUND: The XmR chart is a powerful analytical tool in statistical process control (SPC) for detecting special causes of variation in a measure of quality. In this analysis a statistic called the average moving range is used as a measure of dispersion of the data. This approach is correct for data with natural underlying order, such as time series data. There is however conflict in the literature over the appropriateness of the XmR chart to analyse data without an inherent ordering.METHODS: We derive the maxima and minima for the average moving range in data without inherent ordering, and show how to calculate this for any data set. We permute a real world data set and calculate control limits based on these extrema.RESULTS: In the real world data set, permuting the order of the data affected an absolute difference of 109 percent in the width of the control limits.DISCUSSION: We prove quantitatively that XmR chart analysis is problematic for data without an inherent ordering, and using real-world data, demonstrate the problem this causes for calculating control limits. The resulting ambiguity in the analysis renders it unacceptable as an approach to making decisions based on data without inherent order.CONCLUSION: The XmR chart should only be used for data endowed with an inherent ordering, such as a time series. To detect special causes of variation in data without an inherent ordering we suggest that one of the many well-established approaches to outlier analysis should be adopted. Furthermore we recommend that in all SPC analyses authors should consistently report the type of control chart used, including the measure of variation used in calculating control limits.

Resumo Limpo

ckground xmr chart power analyt tool statist process control spc detect special caus variat measur qualiti analysi statist call averag move rang use measur dispers data approach correct data natur under order time seri data howev conflict literatur appropri xmr chart analys data without inher orderingmethod deriv maxima minima averag move rang data without inher order show calcul data set permut real world data set calcul control limit base extremaresult real world data set permut order data affect absolut differ percent width control limitsdiscuss prove quantit xmr chart analysi problemat data without inher order use realworld data demonstr problem caus calcul control limit result ambigu analysi render unaccept approach make decis base data without inher orderconclus xmr chart use data endow inher order time seri detect special caus variat data without inher order suggest one mani wellestablish approach outlier analysi adopt furthermor recommend spc analys author consist report type control chart use includ measur variat use calcul control limit

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