2.5.6.1. Sensitivity coefficients for measurements on the test item

2. Measurement Process Characterization
2.5. Uncertainty analysis
2.5.6. Uncertainty budgets and sensitivity coefficients

2.5.6.1. Sensitivity coefficients for measurements on the test item

From data on the test item itself

If the temporal component is estimated from N short-term readings on the test item itself

Y₁, Y₂, ..., Y_N

and

s1 = (1/(SQRT(N-1))*SQRT{SUM[i=1 to N](Y(i)-Ybar)**2}

and the reported value is the average, the standard deviation of the reported value is

with degrees of freedom nu1 = N - 1 .

Sensitivity coefficients

The sensitivity coefficient is a1 = SQRT(1/N)

. The risk in using this method is that it may seriously underestimate the uncertainty.

To improve the reliability of the uncertainty calculation

If possible, the measurements on the test item should be repeated over M days and averaged to estimate the reported value. The standard deviation for the reported value is computed from the daily averages>, and the standard deviation for the temporal component is:

s(reported value) = (1SQRT(M))*SQRT{
(1/(M-1))*SUM[m=1 to M](Ybar(mdot) - Ybar(..))**2}

with degrees of freedom nu2 = M - 1 where Ybar(mdot) are the daily averages and Ybar(..) is the grand average.

The sensitivity coefficients are: a₁ = 0; a₂ = SQRT(1/M) .

Note on long-term errors

Even if no day-to-day nor run-to-run measurements were made in determining the reported value, the sensitivity coefficient is non-zero if that standard deviation proved to be significant in the analysis of data.