Critical Process Capability (Cpk)


 

O'PEEP'S CRITICAL PROCESS CAPABILITY EXPLANATION 

The 15 year old son of your neighbor states: "I am as capable as you at driving a car into a garage." Is this true? You are an amazingly great driver? Maybe yes. Yes, if he wants to say that his capability of driving a very small car into a huge double garage is the same as yours driving a really fat car into a really narrow garage.
Yes, process capability describes how good a process is (driving a car into a garage) depending on the requirements (the walls of your garage, the spec limits).  

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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 clover to the center of the specification limits and the lower the spread the better.

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Learn more about setting-up processes to be capable in one of our Green Belt Trainings. Or get the basics for process capability in our eLearnings to process stability.

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