Normal Distribution and IX Charts
The Multiplier for the Mean Moving Range 2.66 and the Multiplier to the Median Moving Range 3.14 used with Individual Value Charts (IX Charts) are both based on a Normal Distribution of the Individual values.The X-Bar Chart, being a chart of Averages, does not really depend on the Individual Values being Normally Distributed. Averages are approximately Normally Distributed regardless (pretty much) of the Distribution of the Individual Values going into the Averages. The same applies to a p-Chart, since a Proportion is essentially an Average. Also, np, u, and c Charts, since they involve a sum or average of Individual Values. All of these, by the Central Limit Theorem, tend to be like Normally Distributed. Even small samples make a big step in this direction.
This is not so for Individual Values. They remain whatever Distribution they come from. And the Control Limits computed for them using 2.66 or 3.14 multipliers of Moving Range Summary Value (Mean or Median) are based on presumption of a Normal Distribution. So it is not surprising that such Control Limits are often unsatisfactory.
posted by X-Bar @ 2:29 PM
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