Attribute charts and capability reporting

I am finishing up with a class and the question came up that they did not understand why we do not recommend a probability plot for attribute yield data.  The students really like to see the variability as the 80% range.  They also want to tell their leadership to expect the yield to fall in that 80% range.

Their motivation is good.  You should be able to give a range of values for yield that indicates a change, but the probability plot is not the right tool.  We use the probability plot with continuous data because the process mean and the process variation (standard deviation) are independent.   A process change is able to change the mean and not change the variability.  This can not occur with a yield or failure percentage.

Binomial (pass-fail) data is limited by a percentage to be between 0 and 1.  This distribution has only a single parameter p, the defect rate, which is equivalent to the average performance.  The standard deviation is a function of the same p and the sample size, actually it is the square root of (p*(1-p))/sqrt(n).

In a simple minitab demo (make two columns of data with binomial random data with a defect p of 0.10.  One has an n=100, one has a n=1000.  covert each to a percentage and then compare the probability plots.  Both have the same defect rate but the standard deviation is quite different.

Same p, different N
Same p, different N

This is the result.  Note the same 50% point but different slopes and standard deviations.  What this means is that the probability plot will show a different range of results based on the sample size.  It is not easy to explain.  That is why we stick to just an i-chart

If you really need to share a range to expect, use the i-chart control limits.  Because if it goes outside of them, it is a special cause indication.  This is better than using a probability plot

Good luck