Solved – Control charts of seasonal data

arimacontrol chart

I have been asked to develop control charts for my company – or some other means of quickly identifying when ticket sales are "out of control" and not just a random blip. The data we are looking at are seasonal with a positive trend (sales revenue).

It has been suggested that I use an exponentially-weighted moving average (EWMA) chart but my (limited) understanding is that these are only appropriate for use on data with a constant mean.

My gut instinct is to apply an ARIMA model and to assess whether observations fall within confidence limits derived from that… but I'm not confident enough to be sure this is the right approach.

My question therefore is:

  1. Is it appropriate to use control charts to monitor revenue sales
  2. What would be the best model to use

Please bear in mind that it needs to be administered by somebody with undergraduate maths, and explained to true lay people.

Best Answer

Should is such a dangerous word. I can tell you how I would approach the problem, but like all answers the mileage is likely to vary.

I'm looking at weather, not sales, but it is highly seasonal. enter image description here

What I did was use a smoothing spline (in MatLab). Here is a link to some more descriptive material. hyperlink (see slides 25-32)

Basic approach is:

  • Sweep appropriate range of smoothing parameter
  • At each point measure AIC
  • Find the local best AIC (non-endpoint, look for actual interior local minimum).

There is some good backing for using this, its applicability to exponential family of distributions that envelopes Gaussian/Normal, Binomial, Lognormal, etcetera, but this is not the place. It is derived from the Kullback-Leibler divergence which comes from Shannon's Information Theory.

So you find the historic mean (thick red line), then you subtract it and use good control material on the re-centered data (right side panels).

Here is the canon for SPC, btw:

If that doesn't work for you, and you want to get deeper, consider this:

Best of luck.

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