Hi,

got a question concerning the rule of seven, which states that when 7 data points fall on one side of the mean, the process is considered "out of control" 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 a zillioin screws a day, you'll run into this situation continuously.

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

Can anyone clarify?

Cheers

Oliver