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Unformatted text preview: IE 361 Module 4 Metrology Applications of Some Intermediate Statistical Methods for Separating Components of Variation Reading: Section 2.2 Statistical Quality Assurance for Engineers (Section 2.3 of Revised SQAME ) Prof. Steve Vardeman and Prof. Max Morris Iowa State University Vardeman and Morris (Iowa State University) IE 361 Module 4 1 / 22 A Relatively Simple First Method for Separating Process and Measurement Variation In Module 2 we observed that One Method of Separating Process and Measurement Variation Figure: One Possible Data Collection Plan for Estimating a Process Standard Deviation, σ x Vardeman and Morris (Iowa State University) IE 361 Module 4 3 / 22 One Method of Separating Process and Measurement Variation Here we will use the notation y for the single measurements on n items from the process and the notation y for the m repeat measurements on a single measurand. The sample standard deviation of the y &s, s y , is a natural empirical approximation for σ y = q σ 2 x + σ 2 device and the sample standard deviation of the y &s, s , is a natural empirical approximation for σ device . That suggests that one estimate the process standard deviation with c σ x = q max & , s 2 y & s 2 ¡ (1) as indicated in display (2.3), page 20 of SQAME . (The maximum of 0 and s 2 y & s 2 under the root is there simply to ensure that one is not trying to take the square root of a negative number in the rare case that s exceeds s y .) Vardeman and Morris (Iowa State University) IE 361 Module 4 4 / 22 One Method of Separating Process and Measurement Variation c σ x is not only a sensible single number estimate of σ x , but can also be used to make approximate con&dence limits for the process standard deviation. The socalled Satterthwaite approximation suggests that one use c σ x s ˆ ν χ 2 upper and c σ x s ˆ ν χ 2 lower as limits for σ x where appropriate "approximate degrees of freedom" are ˆ ν = c σ x 4 s 4 y n & 1 + s 4 m & 1 Vardeman and Morris (Iowa State University) IE 361 Module 4 5 / 22 One Method of Separating Process and Measurement Variation Example 41 In Module 2, we considered m = 5 measurements made by a single analyst on a single physical sample of material using a particular assay machine that produced s = . 0120. Suppose that subsequently, samples from n = 20 di/erent batches are analyzed and s y = . 0300. An estimate of real process standard deviation (unin&ated by measurement variation) is then c σ x = q max & , s 2 y & s 2 ¡ = r max ¢ , ( . 0300 ) 2 & ( . 0120 ) 2 £ = . 0275 and this value can used to make con¡dence limits. The Satterthwaiteand this value can used to make con¡dence limits....
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This document was uploaded on 02/11/2012.
 Fall '09

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