We’ve covered the basics of Z scores here. Basically, we use them to transform a given standard distribution into something that is easy for us to calculate probabilities on. Why? So we can determine the likelihood of some event happening.
We’ve also covered process capability and performance here. Basically, that’s a measure of how centered a distribution is and how dispersed it is.
Naturally, the greater the spread, the less of a chance a process has of meeting its intended specifications.
Practically speaking, Ppk can be determined by dividing the Z score by three. A Z score can be determined by multiplying the Ppk score by 3.
But why? Let’s look at the equations:
A z score is the same as a standard score; the number of standard deviations above the mean.
Z = x – mean of the population / standard deviation.
Cpk = (USL – LSL)/ 6 σ
Ppk = ( USL – µ) / 3σ