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How can I manage the defective rate in this situation?

Discussion in 'SPC - Statistical Process Control' started by judegu, Jul 16, 2018.

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  1. judegu

    judegu Member

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    I have a big question regarding the management of the defective rate(SPC management for attribute data). For variable data, I know we can use X-bar R Chart to do the SPC management. However when it comes to attribute data, it has become tricky. In my original plan I was going to use P chart to do the SPC management. The question is when using p char algorithm (UCL = p-bar + 3* sqtr((1-p-bar)*p-bar/n)) to calculate the UCL, the UCL is so small, almost 10 out of 35 of the points(defective rates) will be above the UCL. It indicates not only the whole process is not statistically stable, but also it is hopeless to do the P chart management. How can I do it with so many anomalies?! Before I was trying to use P chart to manage the defective rate, normally the algorithm for us to caculate the UCL for defective rate is that UCL = average defective rate + 3 * standard deviation of all defective rates. This UCL is large enough that there are not too many anomalies for us to check. The management on this UCL is doable. I know the algorithm of this UCL lacks the correct statistics support, however it can be implemented.
    Please help me on this problem, thank you.
     
  2. Bev D

    Bev D Moderator Staff Member

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    first doing something because it's 'doable' is not worth doing - you will only fool yourself.

    There are several options for appropriate control limit formulas besides the p chart. I would recommend reading Donald Wheeler’s article “What About p-charts?” as a first step in understanding.

    One alternative – depending on what type of ‘defect’ you are trending – is to use the c or u chart. However if you have relatively large sample sizes and your occurrence rate is somewhat low (<5%) this approach is inappropriate.

    The most common reasons for a p chart failing are:

    • The process is actually out of control (even though you can’t find an assignable cause with casual investigation)

    • The process doesn’t follow the ‘model’ for the chart formula (categorical or attribute is much more susceptible to ‘model assumptions’ than the traditional continuous data charts.) Models include Poisson and Normal approximation. This happens for occurrence rates less than ~5%.

    • The sample size is far too high and the defect rate between samples is too large. The fundamental thing to understand here is that ALL control charts work on the assumption that the within sample variation is related to the total variation by the square root of the sample size. In other words the process is homogenous. Many processes are simply not homogenous.

    A control chart actually is designed to detect non-homogeneity. so you are either out of control or you are simply using the wrong formula for your process...using the approach you describe will 'hide' variation and non-homogeneity from you.

    A couple of alternative approaches to try are the I, MR chart (See Wheeler’s “The Chart for Individual Values”) and the p’ chart (See Laney’s “Improved Control Chars for Attributes”. You will have to purchase this article. If you are an ASQ member it is $5 or $10 for a non-member if you buy it from ASQ
     
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  3. judegu

    judegu Member

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    g're'a
    Sir, it is the greatest answer I ever received regarding SPC management so far. Thank you very much.
    "A control chart actually is designed to detect non-homogeneity." You kind of show me the essence of the SPC. Yes, it is all about "homogeneity". Sometime the process just has no homogeneity. The conventional methods simply can't be used in these cases. Or maybe the process being studied is just unstable:(.
    In my case the sample size is always around several thousands pcs and the occurrence rate is definitely below 5%, average occurrence rate is from several thousands to several hundreds of thousands of PPM. We do the full inspection on every production lot by auto inspection machines.
    With regards to the method I talked about, yes, I agree it would hide some anomalies and can't detect all the non-homogeneity. However even using this method, there are enough anomalies detected for us to analyse each day. We are not sampling checking some of the production lots. Instead we check each of them... There will definitely be a lot of anomaly lots detected each day, since we process many of them everyday. I want to know what would you do if you are in my situation. Thanks.:)
     
  4. Bev D

    Bev D Moderator Staff Member

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    I would do what I said I would do above. try the p' chart and the X, MR chart
     
  5. tony s

    tony s Well-Known Member

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    Once you tried Bev D's recommendation, can you post the results of both p" chart and ImR chart here? So we can see the difference.;)
     

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