2. Measurement Process Characterization
2.6. Case studies
2.6.5. Uncertainty analysis for extinguishing fire

2.6.5.7.

Combine the uncertainties into a total uncertainty

Total Uncertainty

The standard deviation for nitrogen volume is the root-sum-square of the uncertainties due to the calibration curve and error in the measurement of flux as follows:

For the samples in the study, the measured values of flux, nitrogen volume fractions and associated uncertainties are shown in the table below. The portion of the uncertainty due to the calibration curve is shown in the 3rd column. The portion of the uncertainty due to flux is shown in the 4th column. The total standard uncertainty is shown in the fifth column.

Table of Uncertainties

Table of measured values of flux (kW/m²) and nitrogen volume fraction (%) and associated components of uncertainty

  Flux    Cal N2 Vol  SD N2 Vol   Due to flux   Total SD
   X         Z                                     

   9.3    34.23508     0.06576     0.20946       0.30488
  10.0    37.40776     0.06259     0.22584       0.30575
   9.6    35.06355     0.06494     0.21647       0.30672
  19.3    46.13260     0.05387     0.45153       0.48476
   4.3    24.34408     0.07566     0.09497       0.29604
   5.0    29.68942     0.07031     0.11074       0.27073
   4.6    21.93403     0.07807     0.10172       0.31322
   5.0    32.50115     0.06750     0.11074       0.25605
   5.4    30.65654     0.06934     0.11979       0.26944
  19.3    45.60766     0.05439     0.45153       0.48527
  17.0    44.51841     0.05548     0.39431       0.43377
  21.4    47.63400     0.05237     0.50458       0.53324
  21.4    46.64503     0.05335     0.50458       0.53408
  30.0    45.06976     0.05493     0.72987       0.75156
   2.1    21.93403     0.07807     0.04598       0.29979
   1.8    21.93403     0.07807     0.03936       0.29884
  12.9    38.86245     0.06114     0.29460       0.35600
  12.5    36.64890     0.06335     0.28503       0.35379
  24.3    47.63400     0.05237     0.57911       0.60424
  25.7    46.13260     0.05387     0.61561       0.64039
  27.1    47.63400     0.05237     0.65246       0.67486