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Rational Sampling

More about the conceptual foundation of process behavior charts

Donald J. Wheeler
Wed, 07/01/2015 - 17:03
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While the computations for a process behavior chart are completely general and very robust, the secret to using a process behavior chart effectively lies in the art of rational sampling and rational subgrouping. Rational subgrouping was the topic of last month’s column. Here we shall look at the broader topic of rational sampling and the bearing it has on the effective use of process behavior charts.

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The first axiom of data analysis

No data have meaning apart from their context. Outside of the statistics classroom, data are always generated by a process or system. They may be the result of an experiment where we manipulate inputs and observe outcomes, or they may be the simple byproduct of ordinary operations where the values are observed as they occur. Regardless of the origin of your data, you have to know their context before you will know how to analyze and interpret them. Thus, the collection of data, the analysis of those data, and the interpretation of the results of the analysis will all depend upon the context for the data.

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Submitted by cliffnorman on Wed, 07/01/2015 - 10:38

Excellent Post

Dr. Wheeler, thanks for an excellent article. As I viewed the examples provided, it reminded of Deming's Forward in my colleague's book, Moen, Nolan and Provost's book, Quality through Planned Experimentation: 

"Any symmetric function of a set of numbers almost always throws away a large portion of the information in the data. Thus, interchange of any two numbers in the calculation of the mean of a set of numbers, their variance, or their fourth moment does not change the mean, variance, or fourth moment. A statistical test is a symmetric function of the data.

In contrast, interchange of two points in a plot of points may make a big difference in the message that the data are trying to convey for prediction.

The plot of points conserves the information derived from the comparison or experiment."

Best regards,

Cliff Norman

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