Relationship between Cpk and Tolerance Interval

When we are making feasibility analysis or designing a new product it’s easy to misevaluate our capacity to attend the quality performance expected.

The main reason is because the design is done with tolerances that can be easily visualized and understood, but the quality performance or quality capability is measured as a ratio Cpk or Ppk that reveals the chances that we have to produce within tolerances.

Normally we just look to the tolerance on the drawing assuming that we can use all the tolerance for our process variation (optimistic approach).

Unfortunately that not true and we are very far away of giving any warranties of getting part within spec to our customer.

In the table below I made one brief compilation of the expected values of the maximum variation admissible in order to attend each Cpk or Sigma level.?

I present 2 scenarios:

• When the average is right on the middle of the tolerance interval
• When the average is half of the way to one side

Below you can find an image with the histogram having the average right on the middle of the tolerance interval (deviation of 0% regarding the tolerance interval).

?And now the histogram having the average half the way to one side of the tolerance interval (deviation of 25% regarding the tolerance interval).

So as rule of thumb and to allow a quick evaluation we can memorize:

• To achieve a Cpk of 1,67 we can only have a process variation of 1/3 of the tolerance interval, if the process is centered.
• If the average is 1/2 of the way to one side of the tolerance, we can only use 1/2 of the variation possible with the process centered.

#processimprovement ;#quality