Applying the Out of Control Tests

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Thanks so much for reading our publication. We hope you find it informative and useful. Happy charting and may the data always support your position.


Dr. Bill McNeese
BPI Consulting, LLC

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Comments (14)

  • Martin GibsonJanuary 31, 2017 Reply

    Hi Bill, as always a good read.  Can you supply the references for the different e=tests please?Thank you and Happy New Year,Martin

    • billJanuary 31, 2017 Reply

      Thank you. Here are two references for the out of control tests:
      Western Electric Company (1956), Statistical Quality Control Handbook
      Douglas Mongtomery. Introduction to Statistical Quality Control

  • MelissaFebruary 4, 2017 Reply

    Thank you for this great read sir. i've searched for so long to find such material to support my spc procedures.  Finally a good find.  Hope you continue these. Really appreciate it. 

  • DaleWMarch 2, 2017 Reply

    Bill, both of your references actually state that 8 successive points in Zone C or beyond (on the same side) is a signal for a non-random pattern.Using the 7 in a row rule gives us a 1 in 64 asymptotic risk of false positives if we have random data — doesn't that seem rather high to you?  Wikipedia even claims that the WECO rule is 9 in a row, which doesn't match their 1956 handbook, athough 9 in a row is more typically in use today (MINITAB default).

    • billMarch 3, 2017 Reply

      Hi Dale.  8 is the most common number.  The WECO rule is 8.   My book has it as 8.  But I shifted it to 7 simply so it matched the rule of seven tests: 7 trending up or down in a row, 7 above or below the average in a row.  I taught this as a good initial set of rules for operators back when we had to do things manually.  Start with that and move to the zones later and wanted the est for zone C to match the 7 in a row.
      The probably of getting this pattern with 7 is .007813 – still pretty small.  With 8 it is .00396 which is closer .0027 of points beyond the control limits.  The software allows you to set the value for the number of points.

  • DaleWMarch 6, 2017 Reply

    Hi, Bill. Actually, the odds of seeing 7 random points in row above or below the established mean is 1 in 64.In Advanced Topics in Statistical Process Control, Donald J. Wheeler claims to personally prefer “nine in a row.” He mentions that Irving Burr expresses the decision rule as “8 to 10 in a row (take your choice).” Wheeler notes “It should be added that virtually all modern authors agree that Grant’s rule [seven in a row] is not sufficiently conservative for good practice.”It’s good to have flexible software.

    • billMarch 6, 2017 Reply

      Thanks for the reply.  7 in a row above the average is .5^7 which is 1 in 128.  Unless I am missing something there.  

  • DaleWMarch 7, 2017 Reply

    Don't forget the either part of the rule.  1 in 128 for 7 above <em><strong>plus</strong></em> 1 in 128 for 7 below equals 1 in 64 for 7 in a row on either side of the centerline.

    • billMarch 7, 2017 Reply

      I will respectively disagree on that.  You are looking at 7 in a row above the average or 7 in a row below the average.  Not the sum of both.   

  • DaleWMarch 7, 2017 Reply

    “If two events are mutually exclusive, then the probability of either occurring is the sum of the probabilities of each occurring.”As an experiment, I ran the 7-in-a-row-on-same-side-of-center-line rule only on a million random normal numbers using Minitab. It took a couple of minutes, but it flagged 15,617 points, which is really close to the theoretical 1 in 64 value of 15,625.

  • eveSeptember 2, 2019 Reply

    Hi!Could you explain further why only the "beyond limits" rule applies to the Moving Average?Planning to create a control chart implementing WECO rules on a moving average.Thanks!

    • billSeptember 2, 2019 Reply

      It is because you are reusing data with the moving averages. For example, each result is used in a subgroup mutliple times.  This means that the data are correlated – they are being reused. So the runs don't apply.  Only point beyond the control limit.   Moving average/range charts often look like cycles.

  • NickJuly 4, 2022 Reply

    How would you establish control charts for processes for which it is hard to assess whether they are in control or not? When talking complaint data, it is not straightforward to estimate whether it is in control or not (how many complaints are 'normal'?). I currently have a dataset which is likely out of control (many complaints), but I'm not sure how to establish a good mean and standard deviation to prove this using a control chart, as the data is so variable. If I take months with many complaints as part of the data, these months will hugely influence the mean and SD, and thus 'allow' for more complaints in subsequent months, which is where I'm getting quite confused. Thanks!

    • billJuly 4, 2022 Reply

      Can you email the data and I will take a look at.  Hard to know without seeing the data.  Thanks.  [email protected]

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