Critical Process Capability (Cpk)


 

O'PEEP'S CPK EXPLANATION 

Your neighbor's 15-year-old son says: “I can drive a car into a garage just as well as you can!”. 
…yesterday he was still driving around here with his plastic tractor, today he is driving grandma's small car into the double garage. There are just as few scratches as when you (experienced car driver) drive your fat luxury vehicle into your tiny garage. Just as rare a scratch? Then the process ability of the boy next door (for his process: grandma's car - big garage) is the same as yours (fat luxury car - mini garage)! 

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The Cpk Index (Critical Process Capability; k: “Katayori”, Japanese for bias) compares the distance from the process center to the nearest Specification Limit (how the process should be) and to the process spread (how it is). 

The greater the Cpk the better the process fits between the specifications. The underlying concept is that a process which is “more on target” is better than a process that is wider distributed. Have a look at the two processes below. Process A is better than Process B (even though through sorting you have the same number of defective items = Out of Specification events) in both processes. 

 

 

If a process is normally distributed the Cpk and process yield respectively scrap rates are linked. For example a Cpk of 1.33 means that less than 0.01% of the total production is scrap. See our table below. 

Cpk correlates with process yield which correlates with DPMO. You can convert Cpk to process yield. Use this table.

ASSUMPTIONS OF THE CPK:

  • Data are representative of the process
  • The process is stable (no special causes)
  • Data are normally distributed


CALCULATION

In the calculation we use the short term standard deviation, sst. This is obtained using short-term data, usually 25-50 samples within a short time frame representing short term variation (i.e. days).

Calculate Cpk Critical process capability. Use this formula. The equation is about Lower and Upper Specification Limit.

This graph on normal distribution, the Gauss curve, explains what is what in process capability. Find an example to calculate Cpk.


EXAMPLES

These normal distribution graphs visualize process capability depending on the spread of distribution and specification limits, upper and lower spec limit.

As you can see, Cpk varies depending on where the center of the distribution is with respect to the specification limits but also depending on the spread (standard deviation) of the distribution. The closer to the center of the specification limits and the lower the spread the better.

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Which processes do we call stable? Are stable processes always good processes? How to deal with special and how to deal with common cause variation? The basics of Process Capability in our fun eLearning.

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