With the release of Minitab V15 you may have noticed that the capability analysis estimated a greate ppm (or percent) out of specification than it did in V14. This is because Minitab changed the default settings for the overall capability analysis. In V14 they used an unbiasing constant to correct the calculated standard deviation. They did not provide an option to take it out.
In V15 the added a check box in the estimate window that allows you to use the unbiasing constant or not. The default was set to be unchecked. If you check the box you receive the same capability output as shown in V14.
Now what is the unbiasing constant? It is easier to show why it is needed than it is to explain with equations. You can use Minitab to demonstrate why it is needed.
Calc>Random Data>Normal… Leave the default settings of 0 and 1.
Generate 2000 rows in 5 column. C1-C5
Now calculate the standard deviation and the variance estimate from each group of 5.
Calc>Row Statistics. select standard deviation, put rows c1-c5 in the box and name it stdev.
now square the stdev column Calc>Calculator. new column = VAR with an equation of Stdev*stdev.
Average both the stdev and the var columns and you will find that the average of the variances is very close to 1.0 (which is what it should be) but the average of the standard deviations is around 0.94. The distribution was set with a variance and a standard deviation of 1.00.
If you calculate the standard deviation of all of the data you will find that it is equal to the capability assessment value with the unbiasing constant not used. (box unchecked)
If you paste these commands into the Minitab Command Line Editor (Cntr-L) Window you can run it yourself.
Random 4000 c1-c5;
Normal 0.0 1.0.
Name c6 “stdev”
RStDev C1-C5 ‘stdev’.
Name C7 ‘VAR’
Let ‘VAR’ = stdev*stdev
Name c8 “Avg Stdev” c9 “Avg Var”
Statistics ‘stdev’ ‘VAR’;
Mean ‘Avg Stdev’-‘Avg Var’.
Let ‘est stdev from var’ = SQRT(‘avg Var’)
What is the correct method to run a capability assessment? The statistical answer is to use the unbiasing constant, as we did in V14. This is the best estimate.
I hope this helps.