Seeing the wood from the trees

I have been working with my colleague, Dave Baker, here at Aviva and we have been researching the long-term behaviour of our processes.

Now I am not going to go down the path of process capability analysis, Cp, Cpk, Zshift and the like. Take a look at this simple time series plot to see why.

Over the long-term some of our processes are extremely seasonal and what we were interested inisunderstanding was how much of the process variation was due to seasonality, long-term trend or random process variation. It has been a bit of the blind leading the blind; we have reviewed statistics books, experimented in Minitab and tried to figure this out.

What we found was Minitab has a capability to decompose the data and with a bit of experimentation we produced an output that showed the seasonal variation and long-term trend.

From this we could eyeball when the process (black-line) moved away from the seasonally expected value (red-line) and also the long-term trend. We then found how to strip-out the seasonal-variation to see the process performance as shown below.

So we believe we have discovered the basics for long-term trendanalysis and some of the benefits appear to be:

  • Ability to see degree to which seasonality affects process performance
  • Ability to better understand long-term trends
  • Gaina clearer picture of process performance without seasonal interference
  • Ability to address short-term customer issues that can be explained by seasonality.

We have some way to go yet but feel we are moving in the right direction and this is getting us a lot of success on a current project.

Comments 4

  1. Ron Pereira

    Cool stuff Robin!

    How did you strip out the seasonal variation?

    Have you played around with the Lowess smoothing factor in Minitab? I have used it before with some luck.

    Time Series > Data View > Smoother > Lowess

  2. Ron Pereira

    Did you use a Decomposition, Multiplicative Model?

    I’d love to see the raw data or something similar to it you are willing to share it.

    Thanks for stretching my mind today!

  3. Robin Barnwell

    Hi Ron

    Glad you got value from this post. It an area not really covered in the LSS BoK.

    As the saying goes, necessity is the mother of invention, having a project with a clear need pushes you to discover new things.

    Good call on the lowess function, we looked at the data using moving average to similar effect, but lowess looks better.

    Yes it was the Decomposition, Multiplicative Model, the stats books talk about 4 components, trend, seasonal, cyclical and process variation, but Minitab does not seem to cover the cyclical component. Still working on how to interpret the results e.g. MAPE, MAD & MSD.


  4. Dave B

    Good to see this went public…

    In general, the value of this tool for me is that you can determine the type of problem you are working on i.e too much process variation, understanding a cyclical process or predicting seasonality.

    So your process looks in control right? Drop into the element layer and test each element, still in control?

    If you know there are seasonal elements in your data set, get rid of them and see how it then looks – do you actually have a process problem (random noise) or do you have a more strategic customer led problem. Can this assist in reducing the risk of a process focused delivery…

    The difference between multiplicative and additive is simple, if we go back to the theory of determinism, decomposition is simply – Yt = f(TCt,St,Rt)

    TCt = Trend Cycle
    St = Seasonality
    Rt = Random Variance

    Additive – Yt = TCt + St + Rt
    Multiplicative – Yt = TCt x St x Rt
    Pseudo-Multiplicative = Yt = TCt(St + Rt – 1)

    If you find the the amplitude of both the seasonal and irregular variations do not change as the level of the trend rises or falls then use an additive model (sure fire if you have removed trend first!!!!)

    All we are looking to do is remove the noise element to isolate the true signal

    Nice one Robin…

Leave a Reply