( ... continued )

When multiplied by 100, Eq. ( 514.43 ) gives the percent error in the simulated strain as a function of the errors or deviations in (the actual gage resistance), , and . Since is ordinarily very large compared to , it can be seen that the percent error in simulated strain is about twice that in the gage resistance, and is approximately equal to that in the calibration resistor and gage factor (although the signs may differ). In practice, the errors in , , and vary independently over their respective ranges of tolerance or uncertainty. Thus, they may tend to be self-cancelling on some occasions; and, at other times, may be additive. The worst-case errors in simulated strain occur when is positive, while and are negative, and vice versa. These conditions can be combined into a single expression by employing the absolute values of the errors:

  (514.44)

Equation (514.44) permits calculating the extreme error in simulated strain from the extreme errors in the other variables. Practically, however, the extreme errors in , , and would occur only rarely at the same time, and with the required combination of signs, to be fully additive. A better measure of the approximate uncertainty (expected error range) in as a function of the uncertainties or tolerances on the other three quantities can be obtained by an adaptation from the theory of error propagation. The latter theory is not strictly applicable in this case because the individual error distributions are unknown, are probably different from one another, and may otherwise violate statistical requirements of the method. However, if the uncertainties in each variable represent about the same number of standard deviations, the following expression should give a more realistic estimate of the uncertainty in than Eq. (514.44):

  (514.45)

where: = percent uncertainty in variable

( continued ... )

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