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

2.6.5.3.

Compute predicted values and standard deviation of predicted values of flowrate

Calibrated Values of Nitrogen Flowrate

Calibrated values of nitrogen flowrate (LPM) are computed as a function of flux from the calibration curve:

From the previous section, this model was determined to be:

Uncertainty for the Flowrate

The standard deviations for the predicted values of flow from the quadratic calibration curve are combined with the residual standard deviation of the fit, S, to estimate the uncertainty for flowrate.

The residual standard deviation is available from the fit outout in the previous section. Dataplot writes the parameter variance-covariance matrix to a file (not shown). For convenience, we print the parameter variance-covariance matrix here:

           a               b              c
a     0.3076035E-03  -0.1132122E-04   0.8771889E-07
b    -0.1132122E-04   0.4565592E-06  -0.3695745E-08
c     0.8771889E-07  -0.3695745E-08   0.3083867E-10

Substituting the appropriate values gives the following formula for the flowrate uncertainty

where

   b0 =  1.0003076
   b1 = -0.0000002264
   b2 =  0.000000632
   b3 = -0.000000003696
   b4 =  0.00003084

Values For New Flux Measurements

Applying these formulas to the new flux measurements results in the following table:

                                SD OF            SD OF
MEASURED  PREDICTED         PREDICTED           FUTURE
    FLUX       FLOW              FLOW             FLOW
      X         Y'              Scal              Sy'
========   =========        =========        =========
     26.   5.2056756        0.0055054        0.0287137
     30.   5.9764223        0.0047473        0.0285781
     27.   5.3996716        0.0052807        0.0286715
     44.   8.5641050        0.0045642        0.0285482
     16.   3.2177362        0.0088804        0.0295471
     21.   4.2226119        0.0069547        0.0290265
     14.   2.8096786        0.0097664        0.0298254
     24.   4.8150678        0.0060222        0.0288173
     22.   4.4209700        0.0066239        0.0289490
     43.   8.3849421        0.0045052        0.0285389
     41.   8.0239973        0.0044005        0.0285225
     47.   9.0963602        0.0047504        0.0285786
     45.   8.7423964        0.0046256        0.0285581
     42.   8.2049055        0.0044501        0.0285302
     14.   2.8096786        0.0097664        0.0298254
     14.   2.8096786        0.0097664        0.0298254
     32.   6.3565612        0.0045103        0.0285397
     29.   5.7850447        0.0049013        0.0286041
     47.   9.0963602        0.0047504        0.0285786
     44.   8.5641050        0.0045642        0.0285482
     47.   9.0963602        0.0047504        0.0285786