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Utilizing Cpk in functional testing



Utilizing Cpk in functional testing

Jukka Antila

It was year 1991 when our production quality manager asked me the question: Could we utilize Cpk in functional testing? I had never before heard of process capability indexes but he also gave me some reading: Keki R. Bhote's book World Class Quality. Among other nice quality tools Bhote explained process capability indexes. Formulas were presented in rather complicated form there, but quickly we could see the power of Cpk in testing. Our company was in telecom industry and in that time functional testing with hundreds of measurements was main method to verify manufactured products. Even though product technologies and test methods have changed a lot from that time, still many features have to be measured from electronic devices in production.
If you have still that same question in your mind, you can find some answers in this text.

For those who are not so familiar with Cpk here we have some background. The formula can be presented in several alternative ways, but I like the following most:

If we assume that measured parameter is normally distributed (as most of them are), we can see from statistical results how well certain test is fulfilling requirements. Couple of samples can tell us how test will behave when volumes are growing.

Distribution examples with different Cpk values.

Everyone knows cases when design engineer has created a product with many nice features. Design has to be verified and here is example how it often goes. Requirement for signal Vout is 4.25 mV to 5.25 mV. First five units (A to E) have been built and tested and we see the results below:
  A  5.0 mV  pass
  B  5.1 mV  pass
  C  4.9 mV  pass
  D  5.0 mV  pass
  E  4.7 mV  pass

Are we satisfied with the design? Most design engineers would be. If we calculate Cpk of these results we get 0.68. From all quality handbooks we know that 0.68 is not good Cpk. But what that means in practice? What that should tell to design engineer?

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