2.4.5. TAB “Results”

Under this TAB selected by mouse click the total result for the output quantity is shown including further variables and the values of the Decision threshold and the Detection limit. The output quantity is indicated which this result is referring to.

These are in detail:

the result of the measurement:

  • the value of the output quantity

  • the expanded uncertainty, in the same unit as that of the output quantity

  • the relative expanded uncertainty (in %)

  • the coverage factor (can be modified in the menu Options)

best estimates according to Bayes and confidence limits

(see also ISO 11929:2019):

  • the value of the output quantity

  • the expanded uncertainty

  • the value of the lower confidence limit

  • the value of the upper confidence limit

  • probability \((1 - \gamma)\) associated with the confidence interval

The toggle button „min. Coverage interval“ can be used to switch the display between probabilistically symmetric and the shortest coverage intervals, also in the case of the MC-Simulation.

Decision threshold and Detection limit:

  • the value of the Decision threshold including the number of iterations (actually no iterations)

  • the value of the Detection limit including the number of iterations

  • the applied quantiles of the normal distribution, \(k_{1 - \alpha}\) and k_beta = \(k_{1 - \beta}\), corresponding to the errors of first and second kind

WLS, PLSQ, PMLE or WTLS: Standard uncertainties of the fitting parameter corresponding to the output quantity from the analysis of decay curve:

  • the uncertainty obtained from the least squares analysis; it is NOT multiplied with \(\sqrt{\chi_{R}^{2}}\) if the reduced Chi-squared value is larger than 1; this variant of the uncertainty of the net counting rate is used for estimating the uncertainty of the output quantity;

  • that value of the uncertainty of the output quantity which is obtained from uncertainty propagation of the arguments of the Linfit function (i.e., mainly the background counting rate, if applicable with blank contribution) and of the uncertainties of the gross counting rates of the decay curve

  • the value of the reduced Chi-square \(\chi_{R}^{2}\)

A Monte Carlo Simulation may be started as a modern alternative to the propagation of uncertainties:

  • input of the number N of simulated calculations of the output quantity (defining one run)

  • input of the number of runs r

  • Optional: selection of the coverage interval of shortest length (shortest coverage interval)

The MC simulation is started by clicking the button “Start”. The iteration number is indicated when iteratively estimating the detection limit.

From the r-fold repetition (runs) means and relative standard deviations (in %) are determined for:

Best estimates according to Bayes:

  • the output quantity

  • the expanded uncertainty

  • the relative expanded uncertainty (%)

  • the lower confidence limit

  • the upper confidence limit

and:

  • the Decision threshold

  • the Detection limit

A new Button “Save values” was introduced. It can be used to transfer all the values being visible in the dialog, including those obtained by MC simulation, together with project name, date/time of execution into a CSV file: UR‑Saved-Results.csv. If this file does not yet exist, it is opened; then, records of data are appended to that file. The meaning of the columns is similar to those of the file AutoReport-Result.csv; however, there are further columns for the LINFIT parameters, for each of the output quantity, the decision threshold and the detection.

In an extra dialog the three distributions are displayed which have been obtained from the Monte Carlo simulation.

In the menu Options one can define the two values of the normal Quantiles corresponding to the errors of first and second kind, respectively. See also Changes within the Options menu.