New control limits that preserve the mean and the skewness of the monitoring statistic

Traditional Shewhart control charts assume that the data generated by the process (or statistics calculated thereof) are normally distributed. This assumption serves as a crude approximation to the true nature of the data generating mechanism, and ignores one of the most important features of the statistic's underlying distribution, namely its skewness. As a result actual performance measures of the control chart (like its false alarm rate (FAR) or average run lengths (ARLs)) do not always conform with the intended design parameters, and the scope of practice of traditional control charts is confined to asymptotically normally distributed statistics only. Furthermore, if recalibrating of the process is performed whenever a shift is indicated by the Shewhart control chart and the statistic's actual distribution is skewed a long term bias in the process parameter may occur. In this presentation we develop the coefficients of the newly defined control limits, recalculate control limits for the range control chart, compare the new control limits to those of traditional Shewhart control charts in terms of ARLs, and examine their performance with respect to some control statistics for which traditional Shewhart control limits are inapplicable. Some alternatives to the use of standard normal fractiles to define probability limits are proposed, and a uniform scale to define shifts in the monitored parameter for non-normal distributions is developed.