Accuracy+and+Precision

Back to Measurement, Uncertainty and Detection Limits

Accuracy and Precision
The two terms are defined in the fig. below:

The Measurement Process
Often the measurand Y is not measured directly, but instead an estimate is calculated from the measured values of other input quantities X1….Xn. These input quantities have a known mathematical relationship to the measurand. In general:

math Y=f(X_1,X_2,X_3....) math Example: Measurement of activity concentration Ac (Bq/g or Bq/L) in a sample may include the gross counting rate (Rs), blank or background counting rate (Rb), counting efficiency () including geometry effect and radiation branching ratio and, test sample weight (w):

math Y=A_c=\frac{R_s-R_b}{\epsilon\cdot W} math

Measurement Uncertainty
When the measurement is performed, a value x i is estimated for X i and an estimated value y of the measurand is calculated using the relationship math Y=f(X_1,X_2,X_3....) math Since there is an //uncertainty// in each input estimate x i, there is also an uncertainty in the output estimate y. The uncertainty of xi is expressed by an //estimated standard deviation (standard uncertainty)// denoted u(x i ). It may also be expressed in the form of an //estimated variance// denoted u 2 (x i ). The ratio u(x i )/|x i | is called the //relative standard uncertainty// of x i.