Table to Find and Propagate Error or Uncertainty to Output from Inputs Based on Formula (Important)
Get unlimited access to the best preparation resource for UGC : Get detailed illustrated notes covering entire syllabus: point-by-point for high retention.
Download PDF of This Page (Size: 149K) ↧
Rules for the evaluation of standard uncertainty through functional relationships with uncorrelated variables. Note how the error for both multiplication and division (6 and 4) is propagated using RMS value.
Rule | Notes (below) | Function | Expression giving standard uncertainty |
1 | |||
2 | |||
3 | |||
4 | |||
5 | |||
6 | |||
7 | |||
8 | |||
9 | |||
10 | |||
11 | |||
12 | |||
13 | |||
14 | |||
15 | , | ||
16 | , | ||
17 | , | ||
18 | , | ||
19 | |||
20 | |||
21 | |||
22 | |||
23 | |||
[(ln (x_{1} / x_{2}))^{2} / (x_{3} − x_{4})^{4}][u^{2}(x_{3}) + u^{2}(x_{4})] | |||
24 | , | (u(y) / y)^{2} = (D_{1}u(x_{1}) / x_{1})^{2} + (D_{2}u(x_{2}) / x_{2})^{2} + (u(a)/a)^{2} + (D_{1}u(b)/b)^{2} + (D_{2}u(c) / c)^{2} | |
25 | |||
Notes:
^{1.}A, B, C, D, D_{1}, D_{2} and N (all upper case) are constants with no uncertainty. They may be integers such as 2 or 3, a decimal number, a mathematical constant such as π, negative or positive.
^{2.}e is Euler’s number and e^{x} is the exponential function. The value of e is approximately 2.7183.
^{3.}log_{10}e is approximately 0.4343.
^{4.}a, b, c, w, w_{1} and w_{2} (all lower case) are uncorrelated (measured) variables with random uncertainty components.
^{5.}x, x_{1}, x_{2}, x_{3}, …, x_{n} are all uncorrelated (measured) variables with random uncertainty components.