Table 15. Sensitivity study of number of voyages.
No. of
IB
Total
IB
Total
voyages and
Time
Speed
escort
cost
Time
Speed
escort
cost
(run time in s)
(hr)
(kn)
(hr)
(US$)
(hr)
(kn)
(hr)
(US$)
West-to-east transits
East-to-west transits
500 (129)
566
5.6
520
720,456
566
5.6
498
713,338
400 (113)
562
5.6
517
715,401
564
5.7
497
712,069
300 (56)
565
5.6
520
719,785
562
5.7
494
708,238
250 (49)
565
5.6
517
717,270
566
5.7
498
714,362
200 (44)
564
5.6
515
716,892
557
5.7
489
701,133
100 (21)
563
5.6
517
717,220
568
5.6
500
716,035
Mean
564
5.6
581
717,837
564
5.6
496
710,862
Std. dev.
1.5
0
2.0
1907
3.9
0.1
3.9
5443
Std. dev. relative
to the mean (%)
0.3
0
0.3
0.3
0.7
0.9
0.8
0.8
500 (repeat)
562
5.6
517
715,153
564
5.6
494
710,236
Table 16. These data include the means and stan-
ages simulated. These results are summarized
dard deviations that were calculated for each
in Table 15.
simulation's 100 voyages. We tested identical sce-
The data show that there is no appreciable ef-
narios in both directions for the months of April
fect due to the number of voyages simulated. The
and August for all three ship types. We then calcu-
variation between runs was extremely small as the
lated the percentage difference, Dn, between each
standard deviations for the categories of interest
pair of values using the formula
were all less than 0.4% of the means. The number
of transits had even less of an effect on the results
Dn = [(westward value/
than repeatedly running the same set of condi-
eastward value ) 1] 100 .
(4)
tions. In fact, when we repeated the 500-voyage
west-to-east case, its results along with the earlier
For example, Dn of the mean speed of a Noril'sk-
500-voyage run bracketed all other runs shown in
class vessel in April is
the table. That is, the transit times of 566 and 562
hours are the extremes, and the same is true for
[(5.53/5.68 ) 1] 100 = 3%
mean ship speed, hours of icebreaker escort, and
total cost of the transit. The variability in all cat-
and Dn of the SD for the mean speed is
egories was greater for east-to-west transits, but
the standard deviations were still less than 1% of
[(0.29/0.36 ) 1] 100 = 19%.
the means.
It is clear from these data that 100-voyage runs
For many parameters, Dn for the SDs are quite
allow for the chance variation to be exercised ad-
high and, in general, those for the means are very
equately in our model. Therefore, all later time
low. This fact shows that the variability between
and cost simulations reported for this study are
each run's 100 voyages is more directionally sensi-
the mean results of 100-voyage runs.
tive than is the parameter itself. Even though
greater variability was apparent, we were mainly
Directionality
interested in the effect of direction on the mean
Comparing the mean values derived in Table
values for our study. The absolute values of Dn for
15, we find little difference between eastward and
the means were all less than 3%, except for ice-
westward transits. The respective means for time
breaker escort hours and this was greatest for a
and speed were identical, and the means for total
Strekalovsky-class ship in August, at nearly 20%.
cost differed by only 1%. We found a significant
The two parameters of greatest interest to this
directionality difference (15%) only in the mean
study were the means for elapsed time and cost.
number of hours that an icebreaker escort would
These were less than 2% in all cases. We concluded
be required.
that with the environmental data we currently
A more robust test of directional dependence
have, there is no significant difference in time and
was conducted, and these results are presented in
36
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