Cp and Cpk are related. Really?

Process capability analysis plays an important role in quality. It helps determine whether the process is capable of consistently producing parts conforming to customer requirements. Cp and Cpk are the two most popular capability indices used to find process capability. Cp and Cpk are related to each other. Whenever I say this most people around me are surprised, some think I am insane. But it is true. Cp and Cpk are related by the equation. Refer to chapter 6 in the NIST/SEMATECH e-handbook of Statistics Handbook

Cpk = (1-k) Cp
where k is the distance between the process mean and the midpoint of specification range.



where
m = midpoint of the specification range or tolerance
mu = process mean
USL and LSL – upper and lower specification limits.

k has a value between 0 and 1.
When k is 0, Cpk is equal to Cp.
When k is less than 1, Cpk < Cp

That is why Cpk ≤ Cp.

Data versus Facts

Taiichi Ohno said "Data is of course important in manufacturing, but I place the greatest emphasis on facts".
Ohno believed that data served as mere indicators of what's going on in the process.
Actually verifying on the scene facts of the situation is key to knowing exactly what's happening.

The Ohno circle requires people to stand in the circle drawn on the floor of a plant for hours to observe the process. This helps the person to gather facts first hand, thoroughly understand the actual situation, then evaluate and analyze what's going on. This is "Go and See the actual situation for yourself" principle practised at Toyota.

At Toyota, nothing is taken for granted. What one sees in person first hand may never show up in reports.
Data in reports may measure results however, it misses out to reveal the details of the actual process that is being followed on a daily basis.
Data can be manipulated, but facts remain hard facts!