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Using K-Factor(Tolerance Interval) Analysis for Design Verification



I am working on a Design Verification project for a customer where the acceptance criteria used for a diameter feature is K-Factor Analysis at 90%/90% Confidence/Reliability (C/R). The idea is that at stated C/R values, once you compute your Tolerance Intervals, they should be within your specification limits (Upper-one sided limit in our case)

Out of 30 datapoint collected recently, 1 point is outside specification. However, the K-factor (or Tolerance Interval) is still within specification limit (as the process average is well within the USL and std. Deviation is very small).

Our team is suggesting that we can chose to ignore the fact that one point was outside specification since the K-factor is still within specification limits! Doesn't this violate the very first requirement to perform any statistical analysis, that is, the data has to be "in control" prior to analysis?

Has anyone else run into this situation? If so, how did you handle this predicament?

Thanks in advance for your help!
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Bev D

Heretical Statistician
Staff member
Super Moderator
can you describe what the 'k-factor' analysis is? I think I know, but I've been surprised by Customer requirements before. It might also be helpful for you to post your data if you can.

The requirement for statistical analysis is not that the data (or process) be in control. but rather that the choice statistical analysis matches the data's true state of distribution.

If you are referring to the traditional process capability study, then yes the process needs to be in a state of statistical control prior to assessing capability; however one point outside of the spec limits is not an indication of instability. again helpful to see your data


Hello Bev,

Thanks for a quick response!

K-factor analysis is used in our facility in lieu of a plain +/- 3-sigma tolerance interval. Here are a couple of good primer on Tolerance Interval- Tolerance intervals for a normal distribution
Statistical Tolerance Intervals | Quality Digest

The idea is that, instead of computing average and std. dev. and then using +/- 3 Std. Deviations to figure out your process spread, the K-factor (or K-multiplier) depends on your sample size. Higher the sample size, lower the K-multiplier is. For the same sample size, the K-factor is different for a one-sided Vs. a two-sided specification limit.

For this analysis, once we have computed Average and Std. Deviation from collected data, we have to figure out what K-factor to use. To get this K-factor value, we have to know what Confidence/Reliability (C/R) value we need to use (which in turn is derived based on the Severity/Occurrence values one has on their FMEA- most companies have such a matrix prepared in their site) and we also need to know the sample size. Then it's just a matter of going to this table and looking for a K-factor value corresponding to the C/R value and sample size. Once K-factor is know, you simply multiply it by the standard deviation and then use it for your "Average +/- K x Sigma" equation to compute the process spread and compare it to your specification limit to ensure that this computed Tolerance Interval is smaller than your specification limit.


Last edited by a moderator:

Ronen E

Problem Solver
Staff member
@vbhatta Thanks for highlighting Dr. Wheeler's article on Tolerance Intervals. I find it extremely enlightening and apparently useful for me.
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