# Translating AQL to a Production Line Inspection Plan

#### Bev D

##### Heretical Statistician
Super Moderator
OK - I worked out the Cp and Cpk values for the data you sent. it is in the attached excel file. I assume that hyou now understand that your formula for Cp was wrong - you were not including the standard deviation.

In general if you look at the histogram of your data there are parts that are out of spec on both sides of the tolerance range. Your process is also not centered. The average is higher than the target.

Cp is a simple ratio of the actual process spread (6*SD) to the tolerance (USL-LSL) (as if it were centered)

Cpk takes the location of the process relative to the tolerance into account in addition tot eh spread vs the tolerance range.

Therefore, unless the process is perfectly centered Cp (aka process potential) will always be greater than Cpk (aka process performance).

Please be advised that this topic is quite complex and I suggest that a few searches for past discussions here will be very helpful in increasing your understandign of the topic...rest assured that you are not the only one who has had these questions and/or who has had less than stellar training...

#### Attachments

• Cp Does Not Always Equal 1.xls
54.5 KB · Views: 161

#### bobdoering

##### Stop X-bar/R Madness!!
Trusted Information Resource
Anyone to help me to solve the question above? Thanks

See attached file.

#### Attachments

• cpk data.docx
161.5 KB · Views: 181
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#### Eric Rco

Wow! Thanks a lot guys. You make my day.

So since the Cp is the centered process and Cpk is the adjusted process, why would we bother with the Cp then if the Cpk is the truth?

I've been told to always look for Cpk 1.33 which I clearly understand why. Not only it will have greater chances to remain within specs if the mean shifts, but you not scratching the car doors even if it is centered. But, if the Cp is below 1.33, why would I even bother to calculate the Cpk? Maybe I'm answering my 2 questions by asking it?

So in order to fix these goods to be in specs, either they fix the making process, either we change the tolerances? I'm I correct?

#### Bev D

##### Heretical Statistician
Super Moderator
Actually there is never any real reason to calculate the Cp. This index is based on the fallacy that it represents the 'inherent process capability' if only one could center the process - becuase centering is easier than reducing standard deviation. HAH! if only that were always true. (and in the more complicated version of short and long term capabilty indices, if only we could center it and reduce the 'assignable cause' variation between subgroups).

Unfortunately the real world is rather more complex than this simple theory...and real world practitioners need real world tools and answers.

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#### Eric Rco

You guys solved all my questions. Many thanks to you! Let me know if you are giving sigma or QC classes one day. I'll attend. Have a wonderful weekend.