# ISU IE 361 - Notes on Elementary Statistical Consider- ations in Metrology (2 pages)

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## Notes on Elementary Statistical Consider- ations in Metrology

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## Notes on Elementary Statistical Consider- ations in Metrology

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Pages:
2
School:
Iowa State University
Course:
Ie 361 - Statistical Quality Assurance
##### Statistical Quality Assurance Documents

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Some Notes on Elementary Statistical Considerations in Metrology The basic Measurement Model display 2 1 page 19 of V J is y x where x is a true value of interest is a measurement error and y is what is actually observed We assume that is a random variable with mean the gauge bias and standard deviation measurement So under this model repeat observation of the same x does not produce the same y Under this model with x fixed Ey x and Vary 2measurement On the other hand with x random varying and independent of x Ey x and Vary 2x 2measurement For a sample of m observations on the same unit with sample mean y and sample standard deviation s Ey x and Es2 2measurement and basic statistical methods can be applied to y and s to produce inferences of metrological interest Consider first the usual confidence limits for a mean s y t m t is based on m 1 degrees of freedom These are limits for x If the gauge is known to be well calibrated have 0 bias they are limits for x the single true value for the unit being measured On the other hand if x is known because the unit being measured is a standard it then follows that limits s y x t m can serve as confidence limits for the gauge bias Then consider the usual confidence limits for a standard deviation s s m 1 m 1 s s 2m 1 upp er 2m 1 lower In the present context these are limits for estimates measurement Finally mostly for purposes of comparison with other formulas we might also note that a standard error for an estimated standard deviation of s is s 1 s 2 m 1 1 For a sample of n observations each on a di erent unit Ey x and Es2y 2x 2measurement Applying the usual confidence limits for a mean sy y t n t is based on n 1 degrees of freedom are limits for x the mean of the distribution of true values for all units plus bias Note that the quantity sy doesn t directly estimate anything of fundamental interest But since q x 2x 2measurement 2measurement an estimate of unit to unit variation free of measurement noise based on a sample of

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