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Exact Answers to the Wrong Questions

Why statisticians still do not understand Shewhart

Donald J. Wheeler
Fri, 03/02/2012 - 13:52
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In a recent article that shall remain nameless, a statistician carefully worked out the exact answer to the wrong question. Then, based on this exact answer, he made an erroneous recommendation regarding the use of a process behavior chart for individual values. In this column I will explain both why the question was wrong and how the recommendation is in error.

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The question that the article claims to answer is, “How does sample size impact Shewhart individuals control chart reliability?” To answer this question the article pulls out a standard tool of statistical inference, the “confidence” interval. These intervals are commonly used to express the uncertainty in an estimate of some parameter. As such, they complement the point estimate of a parameter by expressing the worst-case values that are consistent with the given data.

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Submitted by Bill Sproat on Thu, 03/08/2012 - 15:03

Wheeler correct again

Without getting into too much detail, our process relies on a very delicate instrument to measure a specific product property.  In order to maintain the calibration of the instrument, a known standard is checked weekly to verify calibration and is tracked via a XmR chart.  The known standard degrades over time such that we get only 20 or 30 measurements before it has to be replaced with another known standard.  The result is that each "standard" is slightly different than the previous standard meaning the process is potentially changed with each new standard.

As Dr. Wheeler points out, we can't wait for 30 samples to calculate limits so we calculate them at 3 or 4 samples and then update as we go.  Dr. Wheeler's description of signals and false alarms is right on the money.  The XmR charts behave exactly as described in this article and are very useful.  Our emperical data supports the results of the simulation study very well.  Excellent work!

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