tailieunhanh - Engineering Statistics Handbook Episode 3 Part 15

Tham khảo tài liệu 'engineering statistics handbook episode 3 part 15', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | . Uncertainty for quadratic calibration using propagation of error Propagation of error using Mathematica The analysis of uncertainty is demonstrated with the software package Mathematica Wolfram . The format for inputting the solution to the quadratic calibration curve in Mathematica is as follows In 10 f -b bA2 - 4 c a - Y a 1 2 2 c Mathematica representation The Mathematica representation is Out 10 2 -b Sqrt b - 4 c a - Y 2 c Partial derivatives The partial derivatives are computed using the D function. For example the partial derivative off with respect to Y is given by In 11 dfdY D f Y 1 The Mathematica representation is Out 11 1 2 Sqrt b - 4 c a - Y Partial derivatives with respect to The other partial derivatives are computed similarly. In 12 dfda D f a 1 a b c Out 12 1 - ----------------------- 2 Sqrt b - 4 c a - Y In 13 dfdb D f b 1 http div898 handbook mpc section3 3 of 7 5 1 2006 10 12 26 AM . Uncertainty for quadratic calibration using propagation of error Out 13 b -1 ------------------------ 2 Sqrt b - 4 c a - Y 2 c In 14 dfdc D f c 1 The variance of the calibrated value from propagation of error Out 14 2 - -b Sqrt b - 4 c a - Y a - Y ----------------------------------- - ---------------------------- 2 2 2 c c Sqrt b - 4 c a - Y The variance of X is defined from propagation of error as follows In 15 u2 dfdY A2 sy A2 dfda A2 sa A2 dfdb A2 sb A2 dfdc A2 sc A2 The values of the coefficients and their respective standard deviations from the quadratic fit to the calibration curve are substituted in the equation. The standard deviation of the measurement Y may not be the same as the standard deviation from the fit to the calibration data if the measurements to be corrected are taken with a different system here we assume that the instrument to be calibrated has a standard deviation that is essentially the same as the instrument used for collecting the calibration data and the residual standard deviation from the

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