I am measuring the number of events that happen within n minute intervals for a group of 100 stores. My problem is, I am looking for a way to calculate a threshold for the acceptable number of times this event can occur within the 10 minute interval without some established boundary. Although this is a Poisson distribution can I use process control limits of 3sd? And if I use a process control does that mean my upper control limit is my threshold? And if a value exceeds how should that be interpreted?

  • $\begingroup$ What properties do you want your control limits to have? What makes you say it's Poisson rather than something else? $\endgroup$ – Glen_b Jul 20 '17 at 1:09
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    $\begingroup$ NIST gives advice about control charts for Poisson data. I've had decent success monitoring lower count Poisson series just by taking the square root, see here for some reference to that work. $\endgroup$ – Andy W Jul 20 '17 at 13:19
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    $\begingroup$ @Andy The NIST methods are OK for largish counts. (They recommend a Normal approximation for large counts and variations on the square root transform for moderate counts.) When the counts are low--when a substantial number of zeros appear in the data--then beware. $\endgroup$ – whuber Jul 20 '17 at 14:13
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    $\begingroup$ Agree @whuber. My experience with monitoring crime counts is that they need to have at least a mean of 5. I did some additional simulations of data with overdispersion here, and I found that simply adding 1 sigma tended to produce reasonable coverage, so 2*sigma for normal data ~ 3*sigma for the square roots of the overdispersed crime counts. Not perfect for sure, but appeared to limit false positives in my application to reasonable numbers. $\endgroup$ – Andy W Jul 20 '17 at 14:31
  • $\begingroup$ @Glen_b the description of the problem states why it is a Poisson process. $\endgroup$ – DataTx Jul 20 '17 at 14:41

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