CU-Boulder MCEN 3037 - 10 (18 pages)

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Pages:
18
School:
University of Colorado at Boulder
Course:
Mcen 3037 - Data Analysis
Data Analysis Documents

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Example In the control of a chemical process temperature is measured by a sensor that according to the manufacturer has a calibration of 0 50C In 20 measurements in a test of the temperature sensor s repeatability an average value of 1500C was determined with a standard deviation of 1 50C It is estimated that there can be a spatial variation of 20C and an installation effect of 10C In a separate test of the data transmission system it was determined that for 10 measurements the standard deviation was 0 50C The control program uses a linear relationship between temperature and voltage which can introduce an uncertainty of up to 100C in the applicable range What are the elemental errors classify as B and P calibration B repeatability P spatial variation B installation B data acquisition P linearity B If we put numbers to these we have BIAS calibration 0 50C spatial variation 20C installation 10C linearity 10C Precision repeatability P 1 50C 20 measurements data acquisition P 0 50C 10 Measurements Combine elemental Bias Errors B 52 22 12 22 C 2 5C Combine elemental precision Errors USE SD NOT SDOM P 52 1 52 1 58 C ux B 2 tv P P What is n 1 2 2 ux 2 52 tv P 1 58 repeatability P 1 50C 20 measurements data acquisition P 0 50C 10 Measurements What is tn P t23 95 2 07 P 95 2 K 2 Pk n k K1 4 Pk k 1 vk 1 5 n 2 So we have 1 2 2 4 C 1 2 2 u x 2 52 2 07 1 58 0 Total uncertainty of a single T measurement 4 0 5 vk Nk 1 2 4 1 5 0 5 19 9 2 22 9 23 In the previous example we looked at the uncertainty in a single measurement of temperature based on available data We would use SDOM if we were interested in the best estimate of the true temperature R f x1 x2 x3 We know that R f x1 x2 x3 We need to figure out uR f Px1 Px2 Px3 Bx1 Bx2 Bx3 Again we can divide these elemental errors into Pk Elemental Standard Random Uncertainty Where P is given by P Sx Sx P N We propagate the systematic Single measurement error through L 2 B i Bi i 1 Measurement of the mean We propagate the standard random



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