Introduction
What is Error Propagation? An approximation-based statistical method for estimating the uncertainty in a result based upon the uncertainties in its individual input values. Scientists and engineers can evaluate the confidence of their results, provided they know how errors propagate through calculations.
What is Like SPI, Why Do Error Propagation Really Matter?
Quantification of Uncertainty: It is useful for calculating the bounds on values a quantity may take.
Experimental Design: Helps design of experiments to reduce uncertainties.
The Data Analysis: It helps to understand the meaning of experimental outcome.
Validation of Models: It can be used for validation of the model as well as simulations.
Basic Concepts
Random Error โ Uncontrollable variability in measurements that can be minimized by averaging multiple measures.
Systematic Error: A deficiency in the measurement device that consistently impacts all measurements.
Propagation of Uncertainty: The method used to quantify the uncertainty in an output value when there is uncertainty associated with one or more input values.
Methods of Error Propagation
Propagation of Random Errors:
Sum or Difference: The uncertainty of a sum or difference is the square root of the sum of the squares of their uncertainties.
Product or Quotient: The relative uncertainty is an additive function between two different quantities in a product or quotient of the form ๐ด=๐ถ1ร๐ถ2M=C1รC2We have: โ๐ด๐ด=โ๐ถ1๐ถ1+โ๐ถ2๐2โฎ and so onโฆ
Power Law: The fractional uncertainty in a power of a quantity is the product of both the power and the fractional uncertainty in that variable.
How Systematic Errors are Propagated
So, we know that for a sum or difference such as; u+v or uโv then the systematic error is given by : โ(u +v) = โ[โu2 + โv2]
Relative systematic error in the product or quotient of two quantities: the relative systematic error in the product or calibre of two amounts is a sum.
