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Control Charting Rejected Vials Data

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  • #46186

    boettler
    Member

    I am curious to learn how other manufacturing companies control chart rejects data (e.g. parts, items, or in our case vials with product).  I am referring to the operation of inspection where an automated system separates defective from non-defective vials.  The resulting data is binomial but we can’t use p- or c-Charts because we perform 100% inspection of very large lots (n>100,000 vials) rather than of samples from the lots.  That causes us to use either box-cox transforms to normalize the data, or non-parametric statistics, in order to control chart it.  Both methods have their down sides.  Transformed limits tend to be inflated for the most part (especially when the distributions are tailed), and non-parametric statistics may flag too many out-of-control-limit points (especially when the distributions are tailed).  So, how are other companies that perform 100% inspection controlling their defect rates?  I’d really like to compare notes.  Thanks in advance!

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    #152303

    accrington
    Participant

    Who told you that you can’t use a p – chart? If you know the size of a lot, and you know the proportion defective, you can plot lot – by – lot proportion or % defective. This is simple and immediately gives you an idea of ongoing performance.
    I would imagine that all sorts of people in your organisation would be interested to know how you were doing, and a % defective chart can be easily understood by anyone.
    Best leave the Box – Cox transforms, non – parametric stats, and other mumbo – jumbo to the Six Sigma priesthood, for discussion at the WCBF conferences

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    #152307

    accrington
    Participant

    You’re right, as usual, assuming his proportion defective is small. The I -mR chart would be better

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    #152305

    Ken Feldman
    Participant

    Accrington,
    With such a large n and hopefully a very small number of defective, the p chart will probably not be very useful. The proportion may be very small so the skewness of the resulting binomial will make for a very weird looking p chart. Furthermore, the large n will make the +/- 3 s.d. value very small so the control limits will be very close together. As an alternative, possibly he can plot the proportion on an individual/MR chart.

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    #152309

    boettler
    Member

    Thank you again!
    Your assessment of why p-charts don’t work well is correct.  There are very low defect rates but extremely large N in my case.
    Regarding the I-MR option, wouldn’t the control limits in an I-MR chart assume normality?  If so, wouldn’t the limits be inaccurate given that the distributions are binomial?  That’s why I thought that using either box-cox transformations or non-parametric statistics would produce more accurate limits… please advise.

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    #152312

    accrington
    Participant

    I – mR charts are fairly robust to departures from normality (see Wheeler). If you can get reasonable working limits with an I – mR chart, why bother with transormations,etc, which may not be understood as well by the rest of your organisation?
    If you’ve got MINITAB, you try the different methods out,and see which is best for your process (that’s what I reaad Darth’s reply to my post).
    All models are wrong, but some are more useful than others

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    #152320

    Ken Feldman
    Participant

    Agree that transformations are not the way to go and that I/MR is pretty robust.  I wouldn’t worry about normality at this point especially if the np>5 rule of thumb applies.  Don’t ask me to explain it, check it out yourself.  Of course, I am referring to the original poster and not Accrington :-).

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    #152345

    accrington
    Participant

    Another thought, whilst sat in the pub on the way home from the office last night. Try expressing the proportion defective as number of  defective vials per million. Round to the nearest whole number and plot on an I-mR chart or a p – chart, whichever gives the most sensible limits. That way you get a running record of your process which should be comprehensible to most of your colleagues. It seemed to work when I tried it in MINITAB just now.
    By the way, how many defective vials do you typically get in a batch of 100000?

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    #152378

    John H.
    Participant

    Rob
    If there is a low probability of occurrence, a  c  chart based on the Poisson Distribution should be applicable in this case. You can you use a Chi Square test to determine the applicability ( Expected vs Observed frequencies) of the Poisson vs the Binominal Distributions to your data.
     
    I hope this helps.  
     
    John H.
     

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    #152552

    boettler
    Member

    Thanks again for the replies!
    As far as the total number of defects per 100000 we typically get between 100 to 5000 defects or 0.1% to 5%.

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    #152554

    boettler
    Member

    Again thanks!
    I will try the options you’ve mentioned (I-MR, p-charts, c-charts) and see how the distributions we have look on those charts.  One difficulty we have is the large number of defect categories we track (>100 given different products).  So the distributions and value ranges look very different at times (as I mentioned in my previous message posted, our total defectives can range from 0.1% to 5%) and this can be a challenge in trying to find a single type of control chart to fit all.  But I will try your suggestions and then post how that goes so you’ll know.
    Thanks a million!

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    #152568

    Jim Shelor
    Participant

    Rob,
    From reading this thread, you may have a more difficult problem to contend with.
    You need to check the history of reject detection to see if the rejects tend to be detected in bunches.  That is to say several rejects over a group of 500 vials while little or no rejects occur in the preceeding or succeding 5000 vials.
    This would be an indication that your rejects are not independent.  That is to say the probability of rejection is not equal for each vial in your production line.
    Equality of the probability of rejection is a key characteristic in SPC.
    If your rejects are bunched, a simple run chart without control limits may be your best, or only choice, depending on just how bunched your rejects are.

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    #152572

    Uncle
    Member

    Not independent – what a radical notion …
    don’t remember hearing or reading about that in any Six Sigma training. Are you sure? What might this imply for DPMO, Process Sigma, and z-bench, not to mention the unmentionable!
    I wonder what would happen to ‘control limits’ if there is covariance within a subgroup. Oh! Of course, control limits are based on an economic sample size and not X-bar +/- 3 sigma !!!! :-)
     

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    #152574

    vidyut chandra patange
    Member

    If machine is doing 100% automated inspection, then why have you find need to have control chart, rather concentrate on the defects items inpections again to saggregate types of defects and their quantum in a chart …go for abc analysis ,  to concentrate on the defect prevention measures.
     
     

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    #152626

    Jim Shelor
    Participant

    The usefulness of attribute control charts depends on the assumption that all items in the subgroup have an equal probability of being defective/nonconforming.
    If the defects/nonconformances are occuring in bunches this implys one of two things:

    The failure of one part is causing the failures of the succeeding parts.
    A special cause variation is occuring in the process periodically.
    If the failure of one part is causing the failure of other parts, then not all parts have an equal probability of defect/nonconformance and the attribute control chart may be misleading in the presentation of statistical control.
    See “Statical Quality Control” (Grant and Leavenworth)

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