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Tolerance interval and Ppk

Discussion in 'Capability - Process, Machine, Gage …' started by quinch, Mar 21, 2016.

  1. quinch

    quinch New Member

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    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.
     
  2. Roberticus

    Roberticus New Member

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    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...
     
  3. quinch

    quinch New Member

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    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.
     
  4. Bev D

    Bev D Moderator Staff Member

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    The difference here is that the k factor includes an adjustment that incorporates a confidence interval for the point estimate of the standard deviation. The traditional capability indices do not incorporate any uncertainty in the point estimate of the average or the standard deviation. If you use the k factor you will have a wider interval for your process variation than if you use the standard formula. This will give you a smaller capability index.

    You will not find a source for Ppk = k/3 because this is not a true statement. Not even close. A simple explanation is that Ppk includes the average and the k factor doesn't. So they can't possibly be related by that formula.

    If you google tolerance intervals you will find several credible sources as to what k is and how it is used to determine the 'process width' aka tolerance interval.
     
    quinch and Roberticus like this.
  5. quinch

    quinch New Member

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    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.
     
  6. Bev D

    Bev D Moderator Staff Member

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    I don't understand how they set k=3sigma...k is an alternative multiplier to 3. The phrase "the minimum Ppk that needs to be achieved in order to make the confidence / reliability claim" is nonsensical to me. But then again I really don't understand what they are doing...a drawing would help I suppose, but this seems like a lot of hooey for what is just a simple estimate. and a sample size of 15 is just retarded; it completely ignores that most real processes are non0-homogenous and a any random or small sample taken over a short period of time will be horribly inaccurate and no amount of sophisticated statistics can improve this. I would look at the NIST manual on this topic and especially case 3, which is for a one sided upper specification. Then I would ask the company to work through their example with you.

    This is really a new unnecessary complication for the silly process capability index scam...
     

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