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:

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):

### Measurement Uncertainty

When the measurement is performed, a value xi is estimated for Xi and an estimated value y of the measurand is calculated using the relationship

Since there is an*uncertainty* in each input estimate xi, 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(xi). It may also be expressed in the form of an *estimated variance* denoted u2(xi).

The ratio u(xi)/|xi| is called the*relative standard uncertainty* of xi.

###

The two terms are defined in the fig. below:

These input quantities have a known mathematical relationship to the measurand. In general:

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):

When the measurement is performed, a value xi is estimated for Xi and an estimated value y of the measurand is calculated using the relationship

Since there is an

The uncertainty of xi is expressed by an

The ratio u(xi)/|xi| is called the