Open wollmich opened 5 hours ago
The original Power BASIC program computes the same values which are published in the norm.
The output of the original Power Basic program is:
Calibration: Exponential model function
Results of ISO 6143 method:
b0 b1 b2
-4.8019E+01 4.8024E+01 2.1261E-05
Parameter standard deviations/covariances:
u (b0) u (b1) u (b2) cov(b0,b1) cov(b0,b2) cov(b1,b2)
7.9654E-02 7.2525E-02 3.6210E-11 -5.7679E-03 5.0264E-15 -4.8216E-15
Remaining SSD is: 0.6581
Weighted distances:
# x-value x-dist. y-dist.
1.00E+00 1.00E+00 4.72E-03 -7.32E-02
2.00E+00 1.00E+00 -9.43E-03 8.28E-02
3.00E+00 2.00E+00 1.02E-02 -6.14E-02
4.00E+00 3.00E+00 -3.48E-03 9.88E-03
5.00E+00 4.00E+00 5.60E-02 -1.16E-01
6.00E+00 4.00E+00 -7.84E-02 1.80E-01
7.00E+00 5.00E+00 1.07E-01 -3.00E-01
8.00E+00 6.00E+00 -2.99E-02 5.26E-02
9.00E+00 8.00E+00 7.16E-02 -9.16E-02
1.00E+01 8.00E+00 -2.11E-01 3.55E-01
1.10E+01 1.00E+01 3.01E-01 -3.13E-01
1.20E+01 1.00E+01 -1.69E-01 2.83E-01
Goodness-of-fit measure: 0.3552
##Parameter set##
1 ,-.192039388684634 , 1.13383797215994E-3 , 9.04261166891013E-3 , 1.73967210762675E-6 ,-1.36122844736831E-8 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0
4 , .121277454659124 , 5.12125658707491E-4 , 8.49864074983529E-2 , 1.78213759991065E-2 , 2.36930564399249E-5 , 4.97446268461598E-3 ,-3.82646623367887E-7 , 7.93263966955328E-5 ,-1.17799988802113E-7 , 0 , 0 , 0 , 0 , 0
5 ,-48.0191157688416 , 48.024395987938 , 2.12612133535726E-5 , 7.96536972091994E-2 , 7.25254321703939E-2 , 3.62101038225549E-11 ,-5.76787478877683E-3 , 5.02644503269134E-15 ,-4.82163126249274E-15 , 0 , 0 , 0 , 0 , 0
##End set##
The result of a Monte Carlo simulation with 10000 samples and 10000 optimizations:
b(1) = -(48.1404 ± 3.2425)
b(2) = (48.1461 ± 3.2314)
b(3) = (2.1290e-05 ± 1.2832e-06)
covariance between b(2) and b(1) = -1.0478e+01
covariance between b(3) and b(1) = 4.1446e-06
covariance between b(3) and b(2) = -4.1305e-06
Those results are much closer to the results of Example 3.
So I assume it's a bug in the original Power Basic program.
The results for the coefficients b and the uncertainties of b of Example 3 for the exponential function are different than published ISO 6143:2001 norm.
The results from Example 3 are:
The norm claims, see appendix B.2.3: