Small Samples and Non-Normal Capability


Constable, Gordon K., Ph.D.; Hobbs, Jon R., Ph.D.   (1992, ASQC)   Wright State University, PQ Systems, Dayton, OH 45435

Annual Quality Congress, Nashville TN    Vol. 46    No. 0
QICID: 9825    May 1992    pp. 37-43
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Article Abstract

In previous studies, the authors found problems with using standard deviation and control charts to estimate process capability. Here, they examine Pearson curves and the Johnson translation system to test their suitability for determining true process capability.

Both methods determine the form of the probability density function. Pearson curves use a differential equation and sample data to select the form. The Johnson translation system uses kurtosis and skewness statistics. The authors examined sample data in a Weibull distribution with these methods and compared the results with the same sample data analyzed using normal techniques. The sample data was generated in sets of twenty-five, fifty, and seventy-five. They applied three sets of sigma limits to the sample data sets in fifty replications each (for a total of 450 runs). To determine a mean absolute deviation and standard deviation of error, they calculated the differences between the theoretical areas and those resulting from the different techniques.

They found that, for the three negative sigma limit values, the Pearson and Johnson techniques outperformed the normal procedure. Normal techniques were more accurate for the data set of twenty-five samples, but about the same for the other two sets. Thus, the two adaptive techniques may do as well as or better than the normal.


Pearson system,Non-normality,Johnson curves,Estimation,Control charts,Comparisons,Chemical and process industries,Robust design

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