Dangerous Steps and Statistical Process Control

I wrote about process noise and variation, about the way random noise in a system can make it look as if results have changed, when the truth is that the system hasn’t altered at all.

This is all very clever, it is interesting to know that the system hasn’t changed but it doesn’t answer the question:

“How will I know when things have changed?  How will I be able to tell that there is a difference?”

  • When is a change in the result just random noise?
  • When is a change in the result a real change in the system?

How will I know?

Have a look at the picture below, it is a set of steps in the Yorkshire mill town Halifax.  The steps have been there for a while, they have had a bit of wear and tear, so many people have walked up and down them they have worn into a curve.six sigma normal distribution curve

Most people walk up the middle of the steps, that is why that bit has worn down most

A lot of people walk just to the left or just to the right, those parts of the steps are worn down too.  That is just the way people are, nothing to get too excited about.

If somebody was walking over by the left or right walls that would be unusual, there was probably a change in the system, maybe somebody was coming the other way, maybe they were carrying something, I would be interested to know why.

The repeating curve

The shape of the step is called a normal distribution curve.  It shows up all over the place.

Lots of people drive at 75 mph on the motorway, 80mph and 70mph are hardly surprising, not worth getting excited about,you would look twice though if somebody was doing 110 or 40mph.

There are lots of men in the UK who are 5’10” tall, 5’11” and 5’9” are hardly surprising, not worth getting excited about, you would look twice though if somebody walked past who was 4’10” or 6’10”

Shapes and probabilities

Because the curve is the same shape time after time it is easy to work out the probability of getting a certain result, (I could work out what proportion of the UK population is 5’6”), and because you can work out the probability you can decide for yourself when you are happy to accept that the result is just caused by random noise.

Alternatively the result might be so unusual that you want to check to see if the system has changed, may be you are in Holland not the UK.

And that is Statistical Process Control.
UK Male Height Distribution

You can read about the statistics here.

Image by Tim Green

Comments

  1. Hi James,
    Some great points. From your picture, what I would like to know is why the bottom step is more worn than any of the other steps. In fact, wear seems to be progressive as we go up the steps. Is it that we get lighter as we ascend or heavier as we descend?

    Adrian

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