Calculating Ppk and Cpk. Am I doing this right?


TS Contributor
There is something to that, compared to a culture such as Japan. However, I am seeing changes in certain industry segments. For those in consumer goods that are under intense price pressure, I would agree with you. However, in industries where you must maintain high reputation to keep major customers, are exposed to potential litigation, have product life expectancies of 15-25 years, etc., quality and reliability are taken very seriously.
Hi again

Back from holiday - I was thinking. Are there any way that tolerances should be part of these equations? The guy down at the department is not happy with me suggesting that they might also use the range chart as opposed to a combined X-bar and range chart. He tells me that I need to take tolerance into account regarding the range chart, otherwise the UCL will not be useful. I have difficulty seeing the logic in this.

Thanks again!


TS Contributor
Specifications only apply to the capability analysis (i.e., Pp/Ppk, Cp/Cpk). Tolerances have ABSOLUTELY NOTHING to do with the control charts. The control limits are based on the process variation NOT on the specifications.

You can be:
  • In control, in specification
  • In control, out of specification
  • Out of control, in specification
  • Out of control, out of specification
They are independent of each other. Control chart tell you whether the process is stable and predictable. Capability tells you how well it can meet the specification.
Thank you for the very clear and precise answer! I think we have a few shortcomings at my end. I really appreciate your help, and I am trying my best to understand.

As an example, for another set of data than the original in this thread, I have compared the output of out statistical software with the output of R using the qcc-library. I would like to ask you to observe the control limits. In the output (see picture 1) from our statistical software, the control limits are on either side of the target value, even though this puts them both below the X-bar-bar. I was under the impression that one would calculate the control limits from the x-bar-bar (X-bar-bar +/- (A2*R-bar). Thus, the control limits should be above and below X-bar-bar - not the target.

When doing the same data in R (see picture 2), the control limits are above and below the center line (X-bar-bar). This seems right to me. Maybe I am missing something important, that makes me draw the wrong conclusion. Something just seems wrong with the T, X-bar-bar, UCL and LCL in picture 1.

Picture 1. Output from our statistical software

Picture 2. Output from R


TS Contributor
The control chart in Picture 2 is the standard Shewhart control chart with control limits based around the process mean (XdoubleBar).

The control chart in Picture 1 is a specialized control chart with a lot of modifications:
  1. The control limits are based around the desired target value (usually the center of the specifications, or a nominal value). This may be used when the process mean is easily adjusted to a desired setting. If the process is not easily adjusted, this should not be used. See Dr. Wheeler's discussion of this for XMR charts.
  2. Specification limits should never be included on a control chart, particularly on an Xbar/R chart. It can lead to a false sense of comfort and take the urgency away from addressing special causes.
  3. The vertical bars appear to be a visualization of the subgroup max and min spread to avoid creating an R chart. The problem with this is that you will not know when the subgroup Range exceeds its control limit. Even if you could change the color of the line for out of control, you would not be able to see trends or runs in the range.
Dr. Wheeler studied with Shewhart and Deming and has many excellent articles and books on his website.