Tolerance interval and Ppk

I would like to know if there is an accessible source confirming if the following statement is true;

The relationship between normal tolerance intervals (k factors) and process capability index (Ppk) is as follows: k = 3 x Ppk or Ppk = k/3.

In my work I have to assess process validation documentation and recently I have seen this statement in use from a number of external suppliers. My google fu has failed me on finding a source, none of the suppliers can provide one ( SOP's were written by previous employees or consultants).

In the absence of a source perhaps someone could confirm if the statement is true or false and possibly provide some background.

 

I am not familiar with "k factors" but the relationship described is the same as that of your z score, that is to say, if you have a z of 6 (or six standard deviations in either direction between your mean and spec. limits) you come out with a Ppk of 2, or a "6 sigma process".

Maybe the "k factor" terminology is industry-specific? I've never heard of it in medical device nor automotive requirements, nor my Black Belt training...

 

I don't have any of my notes or Minitab to hand but I had not considered a relationship between the Z Score and Tolerance interval. I'll do some more reading with that in mind.

We use the formula T.I = xbar +/- k*sigma to determine what proportion of values lie with the specification limits for a given confidence level[ k is determined from a table] and when data is normal.

 

Thanks, I'm comfortable enough with using capability and Tolerance intervals to assess data, but I'm mostly self taught , no formal study or even green belt- i have read the notes though.

I managed to find someone in the vendors organization to answer, the reply is as follows;

for a 1 sided Spec. with 95% confidence and 99% reliability the target Ppk value is 1.17 using a sample size of 15. This equates to a k factor of 3.52 based on the k tables, The K factor reduces as the sample size increases, as with more data the width of the confidence interval reduces. As the Ppk is calculated from the K factor, the Ppk value also reduces as sample size increases.

The /3 is based on the Ppk calculation (e.g. Xbar – USL/ 3 sigma). With the k Factor set to = 3sigma this will give the minimum Ppk that needs to be achieved in order to make the confidence / reliability claim.

They also claim this is stated in procedures of a major medial device company......

This seems to check out on a surface level, and I'm not confident in my limited stats knowledge to challenge it, how would you approach responding to this? If that is not too much to ask.

 

Hi, I appreciate many years have passed but I'm interested in this topic too...

I'm no expert here, maybe a 5/10! I think there is some confusion though so allow me to rephrase things a little. As I see it, the intent of the original post is:

• Lets assume the correct use of k factors (N, confidence, reliability are used to determine a k factor, lets say of 4.5)
• Now we know the k factor is 4.5 (interval is Xbar ± k x sigma) how could we write this differently to simplify the calculations?
• We could say the equivalent is to say the target Cpk is 4.5/3 = 1.5

To me this makes sense, but people get upset at the misleading use of process capability (which I concede is misleading, but is only used for simplicity)

I concur that I've seen this approach used routinely in medical device companies, including several big names.

Thanks