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In metrology, the law of error propagation is a crucial concept that describes the relationship between the error in the direct observed quantity and the error in the direct observed measurement function. This law provides us with a mechanism to understand how measurement errors are transmitted during the calculation process, which helps us to better control errors and improve measurement accuracy.
The law of error propagation is based on three basic assumptions:
1.The random error is independently and equally distributed.
2.The distribution of random errors obeys a normal distribution.
3.The middle error of the observations is proportional to the arithmetic mean of the observations.
When applying the law of error propagation, there are a few things to keep in mind:
1.The law of error propagation only applies to the transmission of random errors, not to the transmission of systematic errors.
2.When calculating the observed values, it is necessary to ensure the correctness of the calculation and avoid the error caused by human factors.
3.For different observations, the error may be different, so the error in each observation needs to be considered separately when performing the calculation.
In the law of error propagation, if there is a medium error in a direct observational measurement, then the value of the function calculated from this observation measurement will also have a medium error. The magnitude of this error depends on the magnitude of the error in the direct observation measurement and the sensitivity of the function to the change in the observational measurement. This means that during the computation, the error will magnify with the complexity of the computation. Therefore, we need to pay special attention to those functions that are sensitive to changes in the observation measurement to avoid excessive amplification of errors.
The importance of understanding the law of error propagation lies in the fact that it can help us to take appropriate measures to reduce errors and improve measurement accuracy during the measurement process. For example, we can choose the appropriate observation method, optimize the data processing process, use more accurate measurement equipment, etc., to reduce the error in direct observation. At the same time, we can also reduce the transmission of errors in functions through reasonable function design and data processing methods.