Normality

In CM4D, the term Normality refers to the type of distribution that represents a set of individual cell values contained in a DataSet row for a single process. If the values represent a normal distribution, normality is considered normal; otherwise normality is considered abnormal and will represent some other type of distribution.

Normality does not refer to the distribution state of subgroups as subgrouped, data due to the central limit theorem, may be normally distributed when individual cell values are not.

Since it may not be desirable to display Cp/Cpk and Pp/PpK when the individual cell values are not normal, CM4D has a DataSet option to check the normality state before calculating these statistics. If turned on, this option will prevent Cp/Cpk and Pp/PpK reporting when individual cell values are not normal.

CM4D uses two methods to determine normality:

1.     Normal probability correlation coefficient test for normality:

This method uses the correlation coefficient of the data as compared to the predicted normal distribution of that data. A correlation coefficient target value is compared to the calculated correlation coefficient according to the table of critical values below. The table of critical values uses a significance level of 10%. If the calculated correlation coefficient is equal to or greater than the target value, this test will consider the distribution as normal. The results of this test are reportable with the ~distribution~ variable.

The correlation coefficient can be reported using the variable ~cc~, and the target value can be reported using the variable ~cctarget~.

2.     D’Agostino Pearson omnibus test for normality:

Another method uses the D’Agostino-Pearson omnibus test with a significance level of 10% to determine normality. This test first computes the skewness (how asymmetrical is the distribution) and the kurtosis (how far away from a Gaussian/standard normal distribution shape). It then calculates how far each of these values differs from the value expected with a Gaussian distribution, and computes a single P value from the sum of the squares of these discrepancies. This test will result in a normal or abnormal determination. The results of this test are reportable with the ~dagostino~ variable.

If either of these tests determine that the tested data is normal then normality is considered normal. Normality is reported using the ~normality~ variable.

Recommended additional information:

For more detailed information on normality and other statistical areas relating to statistical process control, please refer to the National Institute of Standards and Technology.

Some helpful web links have been provided below:

·        Online Engineering Statistics Handbook: http:// www.itl.nist.gov/div898/handbook/ index.htm

·        Normal Distribution: http:// www.itl.nist.gov/div898/handbook/ eda/section3/eda3661.htm

·        What is meant by "Normal" data: http:// www.itl.nist.gov/div898/handbook/ pmc/section5/pmc51.htm