The purpose of this introductory article is to discuss the experimental uncertainty analysis of a derived quantity, based on the uncertainties in the experimentally measured quantities that are used in some form of mathematical relationship ("model") to calculate that derived quantity. The model used to convert the measurements into the derived quantity is usually based on fundamental principles of a science or engineering discipline.
The uncertainty has two components, namely, bias (related to accuracy) and the unavoidable random variation that occurs when making repeated measurements (related to precision). The measured quantities may have biases, and they certainly have random variation, so that what needs to be addressed is how these are "propagated" into the uncertainty of the derived quantity. Uncertainty analysis is often called the "propagation of error."
It will be seen that this is a difficult and in fact sometimes intractable problem when handled in detail. Fortunately, approximate solutions are available that provide very useful results, and these approximations will be discussed in the context of a practical experimental example.
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