New Control Limits that Preserve the Mean and the Skewness of the Monitoring Statistic


Shore, Haim   (1991, ASQC)   Tel-Aviv University, Tel-Aviv, Israel

Annual Quality Congress, Milwaukee WI    Vol. 45    No. 0
QICID: 9609    May 1991    pp. 77-83
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Article Abstract

This abstract is an edited version of the author's original.

Traditional Shewhart control charts assume that data generated by the process are normally distributed. This assumption 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. If recalibration of the process is performed whenever the Shewhart control chart indicates a shift and if the statistic's actual distribution is skewed, a long-term bias in the process parameter may occur.

This paper develops the coefficients of redefined Shewhart control limits, recalculates control limits for the range control chart, compares the new control limits to those of traditional Shewhart control charts in terms of ARLs, and examines their performance with respect to some control statistics for which traditional Shewhart control limits are not applicable. The author also proposes some alternatives to the use of standard normal fractiles to define probability limits and develops a uniform scale to define shifts in the monitored parameter for non-normal distributions.


Control charts,False alarm rate (FAR),Shewhart, Walter A.,Statistical process control (SPC),Statistics,Control limits,Variation,Average run length (ARL)

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