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I am trying to create a control chart for metrics that are essentially increasing over time. If I attempt to create a Shewhart chart, there will be many points that are above the upper specification limit.

So for example,

My metric is Revenue. Since it is a fast growing company, Revenue is going to be increasing over the specification limit over time. The main thing I want to track is when it is below the lower specification limit.

I know this is very vague but essentially I want to create a control chart that has data increasing over time.

Thanks

Nick Knauer
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    If you yourself already find it vague (and you know your project), how are other supposed to help you? You can make it a lot easier for people to help you by providing a [reproducible example](http://stackoverflow.com/questions/5963269/how-to-make-a-great-r-reproducible-example). – Heroka Sep 15 '15 at 14:56
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    I'm not sure a control chart is the right tool here. A control chart is used to evaluate a process that has, ideally, a predictable result. Revenue of a growing company isn't going to be very predictable. Honey Dipped Badger's answer gives you an option for determining if revenue has dipped below an arbitrarily chosen specification limit. Another option might be to fit a curve through the data and look for places where the slope goes from being greater than 1 to less than 1, or to look for non-monotonic behavior. – Benjamin Sep 15 '15 at 15:04

3 Answers3

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Besterfield in his book Quality Control, sixth edition answers this question. He discusses this as a "Chart for Trends".

Chart for Trends created in Excel

The process involves regression to determine the slope of your center line. The equation is $$\overline{X}=a+bG$$ where $\overline{X}$ is the subgroup average, G is the subgroup number, a is the intercept, and b is the slope.

$$a=\frac{(\sum \overline{X})(\sum G^2)-(\sum G)(\sum G\overline{X})}{g\sum G^2-(\sum G)^2}$$

$$b=\frac{g\sum G \overline{X}-(\sum G)(\sum \overline{X})}{g\sum G^2-(\sum G)^2}$$

where g is the number of subgroups.

The coefficients of a and b are obtained by establishing by columns for G, $\overline{X}$, G$\overline{X}$, and G^2 … ; determining their sums; and inserting their sums into the equation.

Once the trend-line equation is known, it can be plotted on the chart by assuming values of G and calculating $\overline{X}$. When two points are plotted, the trend line is drawn between them. The control limits are drawn on each side of the trend line a distance (in the perpendicular direction) equal to $$A_2\overline{R}$$ …

The R chart will generally have the typical appearance… However the dispersion may also be increasing.

Besterfield also suggests having a URL and LRL or Upper Rejection Limit and Lower Rejection Limit as lines parallel to the horizontal axis and indicate times when the process would be unacceptable.

Insert the codes between the "$$" into the Online LaTeX Equation Editor if you would like to visualize the equations easier (a limitation of my reputation and this page).

Tavrock
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  • This is great and very detailed. Thank you. I'll try it out in excel and look to transfer it over to R in the future – nak5120 Dec 07 '16 at 04:23
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Dropped by here today; it’s an old question that probably has been answered. If not, try a seasonality analysis and plot your deseasonalised séries (tendence removed) on a control chart tool like qicharts2 (in R). If you need more details, just let me know, I can elaborate a more detailed answer.

Juan Riera
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Sounds like plot() is your game here. Time on the X, revenue on the Y with an abline(h= ) for your specification limit. Set a horizontal line where your specification limit is and you are good to go.

Badger
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