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Is The Rule Of Seven Really Valid?


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#1 Klaas2015

Klaas2015

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Posted 09 January 2015 - 03:36 AM

The rule of seven states, that when 7 data points fall on one side of the mean, the process might have a problem and the PM should have a look.

Now, 7 data points on one side of the mean might not be an unlikely event at all - in fact, it's quite likely to occur frequently, depending on your production output:

Let's assume a symmetrical distribution, i.e. the probability that a data point value is greater or less than the mean is both 0.5.

Let's also assume that events are not correlated (which should be the case for a perfectly functioning production line), i.e. the outcome of a measurement does not depend on the previous measurement.

In this case, the probability that 7 consecutive data point values are greater than the mean is (0.5)^7 = 1/128 - that's a bit less than 1%.
The probability that 7 consecutive data point values are on either side of the mean is even greater, namely 1/64 - or about 1.5% (chose any data point - the probability that the 6 consecutive points are on the same side of the mean is 0.5^6.)

In other words: on the average every 64th data point in your diagram starts a sequence which breaks the rule of seven. If you produce 10 bicycles a day, that's not much of an issue. But if you produce 10,000 screws a day, you'll run into this situation a couple of times per hour.

So, under the premises of my assumptions, this rule doesn't make sense, so there must be more assumptions, which I'm missing.
Comments anyone?

Cheers
Klaas




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