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Likelihood Distribution of Number of SpaceX Launches in 2015
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Topic: Likelihood Distribution of Number of SpaceX Launches in 2015 (Read 14683 times)
Proponent
Senior Member
Posts: 7240
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Re: Likelihood Distribution of Number of SpaceX Launches in 2015
«
Reply #20 on:
01/05/2015 08:34 pm »
Proponent: 0 0.0 0.0 0.1 0.2 0.3 0.6 1.3 2.8 5.6 9.4 13.3 15.7 15.7 13.3 9.7 6.1 3.3 1.6 0.7 0.2 0.1
Rationale:
I start from SpaceX
launches listed by Salo list for 2015
, which is more or less consistent with the last with-dates manifest published by SpaceX (attached):
January 6 - Dragon SpX-5 (CRS5) - Falcon 9 v1.1 - Canaveral SLC-40
January 29 - DSCOVR (Triana) - Falcon 9 v1.1 - Canaveral SLC-40
February 17 (TBD) - Eutelsat 115 West B (Satmex 7), ABS 3A - Falcon 9 v1.1 - Canaveral SLC-40
April 8 - Dragon SpX-6 (CRS6) - Falcon 9 v1.1 - Canaveral SLC-40
June 13 - Dragon SpX-7 (CRS7) - Falcon 9 v1.1 - Canaveral SLC-40
1st half - TürkmenÄlem 52.00E (MonacoSat) - Falcon 9 v1.1 - Canaveral SLC-40
2nd quarter - SES-9 - Falcon 9 v1.1 - Canaveral SLC-40
NET 1st quarter midyear - Orbcomm G2 (x11) - Falcon 9 v1.1 - Canaveral SLC-40
August - AMOS 6 - Falcon 9 v1.1 - Canaveral SLC-40 (or 3rd quarter)
September 2 - Dragon SpX-8 (CRS8), BEAM (Bigelow Expandable Activity Module) - Falcon 9 v1.1 - Canaveral SLC-40
2nd half - JCSat-14 - Falcon 9 v1.1 - Canaveral SLC-40
4th quarter - Eutelsat 117 West B (Satmex 9), ABS 2A - Falcon 9 v1.1 - Canaveral SLC-40
December 9 - Dragon SpX-9 (CRS9) - Falcon 9 v1.1 - Canaveral SLC-40
3rd quarter - Demo Flight - Falcon Heavy - Kennedy LC-39A
March 31 - Jason-3 - Falcon 9 v1.1 - Vandenberg SLC-4E
September - SAOCOM-1A - Falcon 9 v1.1 - Vandenberg SLC-4E
late - Iridium Next Flight 1 (x10) - Falcon 9 v1.1 - Vandenberg SLC-4E
late - Iridium Next Flight 2 (x10) - Falcon 9 v1.1 - Vandenberg SLC-4E
TBD - FORMOSAT 5 - Falcon 9 v1.1 - Vandenberg SLC-4E
Let me work backwards through the launch sites, beginning with VAFB. Two launches there seems feasible, but stuff can easily happen. I'm going to guess a triangular distribution centered on two and extending from zero to four. In other words, for VAFB launches I'm assigning likelihoods of
No. Launches: 0 1 2 3 4
Likelihood: 11 22 34 22 11%
Then there's the Falcon Heavy from KSC. I'm pretty sure that's just not going to happen this year, and I'll translate "pretty sure" to 85%.
Now, for the hard part: orbital launches from the Cape's LC-40.
The mean time between Falcon 9 v1.1 launches to date is about 58 days, assuming CRS-5 goes ahead tomorrow (see the plot below, CRS flights are shown in red).
Even if we assume look only at the four most recent flights (and assume CRS-5 goes off as planned), the mean drops just to 44 days. That would leave time for nine flights in 2015, given CRS-5 early in the year. But getting the pad abort test off the ground has got to be important, and that will soak up resources (at least vis-a-vis CRS flights), even if it doesn't actually occupy the pad itself. Maybe, with the burdens of the abort test (I'm guessing there is little chance of the in-flight abort test occuring in 2015), SpaceX could still hope to achieve the same number of orbital launches it pulled of from LC-40 in 2014. But for the modal case, I'll guess that there are six launches total, again, with just five to orbit. Again, I'll go with a triangular distribution, this time with a half-width of 3 rather than 2. So, my LC-40 likelihood distribution looks like:
No. Launches: 3 4 5 6 7 8 9
Likelihood: 6 12 19 26 19 12 6 .
I took the launch intervals from the last 5 F9 v1.1 launches and resampled 100,000 times to get a distrubution for the number of launches from LC-40 in the next year, allowing for the fact that one launch has already occurred with 355 days to go in the year. The result is:
No. Launches: 2 3 4 5 6 7 8 9 10 11 12 13 14
Likelihood: 1.0 0.9 1.0 2.3 8.6 17.7 21.8 19.4 13.7 7.7 3.6 1.5 0.5%.
These won't add to precisely 100%, because I've rounded off and have omitted values less than 0.1%. All values were used, without rounding, in the next and final step.
Convolving all three distributions and rounding to the nearest 1% (thereby eliminating a non-zero likelihood of 14 launches) gives
No. Launches: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 12 13 14 15 16 17 18
Likelihood: 0.0 0.0 0.1 0.2 0.3 0.6 1.3 2.8 5.6 9.4 13.3 15.7 15.7 13.3 9.7 6.1 3.3 1.6 0.7 0.2 0.1
There is some possibility that a catastrophic failure early on will shut SpaceX down for the rest of the year. Accordingly, I steal 1% of likelihood from each of the the two most likely outcomes and redistribute it to the cases of one and two launches:
No. Launches: 1 2 3 4 5 6 7 8 9 10 11 12 13
Likelihood: 1% 1% 1% 2% 6% 12% 17% 18% 17% 13% 8% 3% 1% .
There could, of course, be a massive failure before the very first launch, but I put the probability of such a thing at under 1%, so I'm not going to consider it.
I'm guessing that core availablility won't be a problem. Had I come up with significant likelihoods for, say, 20 launches, I might have pruned the higher numbers to reflect the risk of manufacturing bottlenecks. But after just six launches in 2014, I'm willing to guess that the supply of cores won't be a limiting factor for ten-ish or fewer launches in 2015.
EDIT: After updating my calculation quite a bit, I neglected to put the new results on the first line (though they were already in the body of the post).
«
Last Edit: 01/19/2015 03:06 pm by Proponent
»
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schaban
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Posts: 180
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Re: Likelihood Distribution of Number of SpaceX Launches in 2015
«
Reply #21 on:
01/05/2015 10:11 pm »
schaban: 3 2 4 6 7 8 10 15 20 15 10 2 1
They have to attempt to fly at least 3 CRS missions. Almost a given to have more attempts than previous year.
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Robert Thompson
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Re: Likelihood Distribution of Number of SpaceX Launches in 2015
«
Reply #22 on:
01/06/2015 01:40 am »
0 1 1 1 3 5 8 11 14 14 14 11 8 5 3 1
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Proponent
Senior Member
Posts: 7240
Liked: 2745
Likes Given: 1441
Re: Likelihood Distribution of Number of SpaceX Launches in 2015
«
Reply #23 on:
01/19/2015 03:07 pm »
The poll is now closed to new entries.
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Proponent
Senior Member
Posts: 7240
Liked: 2745
Likes Given: 1441
Re: Likelihood Distribution of Number of SpaceX Launches in 2015
«
Reply #24 on:
01/20/2015 03:42 pm »
First of all, thanks to everyone who took the time to contribute an entry.
Now that the poll has closed, let's use this thread for discussion rather than the poll's
previous discussion thread
. This way, the raw data will be readily at hand should anyone wish to refer to them.
To better reflect the information available at the time of the polls' closing, I have taken the liberty of removing from each any probabilities or votes assigned to zero launches for 2015, since one launch took place before closing. In the
single-vote poll
I have interpreted the one vote for 21-25 launches as 0.2 votes for each of 21, 22, 23, 24 and 25 launches. The one vote for more than 35 is interpreted as a vote for 36.
Firstly, some statistics:
Poll
Size
Mean
Entropy (bits)
Likelihood distribution
22
9.64
3.60
Single vote
666
10.83
3.12
The mean of the likelihood distributions is plotted here, as black bars, along with the single-vote distribution, as red circles. The vertical dashed lines show the means of the two distributions. Obviously the single-vote poll is the more optimistic of the two.
One might wonder how much of the "signal" in the likelihood-distribution poll comes from the spike at 4 launches. That likelihood comes largely from a very manly zero-entropy prediction by saliva_sweet!. Without saliva_sweet's entry, the mean rises a bit to 9.91 and the entropy falls slightly to 3.54. Even then, this poll is more skeptical than the single-vote poll.
The table below summarizes individual likelihood distributions, in order of the distribution mean.
Mean
Entropy
MEAN
9.64
3.60
saliva_sweet
4.00
0.00
Hernalt
7.93
3.43
arachnitect
8.33
2.79
averagespacejoe
8.35
2.79
Garrett
8.45
2.60
CraigLieb
8.47
2.78
Tass
8.61
3.12
skybum
8.75
2.91
schaban
8.90
3.23
Jimmy Murdok
9.29
2.72
toruonu
9.37
3.47
sdsds
9.53
3.82
NaN
9.88
3.00
topsphere
10.17
3.37
cscott
10.89
3.25
nadreck
10.98
3.66
Billium
11.25
3.21
Proponent
11.54
3.40
mheney
11.66
2.81
MikeAtkinson
11.77
3.60
Lar
11.95
3.65
aameise
12.00
3.52
Now it's up to SpaceX to deliver the results!
«
Last Edit: 01/20/2015 10:22 pm by Proponent
»
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saliva_sweet
,
NathanSyn
and
deruch
like this
Proponent
Senior Member
Posts: 7240
Liked: 2745
Likes Given: 1441
Re: Likelihood Distribution of Number of SpaceX Launches in 2015
«
Reply #25 on:
01/02/2016 07:30 am »
Now that the number of SpaceX launches intended to reach LEO or beyond in 2015 is known, scores can be assigned. The columns in the following table respectively show the mean of each participant's likelihood distribution, the entropy of the distribution (zero meaning that all likelihood was assigned to a single number of launches, while larger values indicate greater uncertainty), the likelihood (L) assigned to the actual number of launches (7), and the natural logarithm of that likelihood (lnL). The table is sorted by likelihood. Not only is there a row for each participant, but results are also shown for the mean of all likelihood distributions and for the single-value poll (not included in the mean).
Mean
Entropy
L
lnL
Garrett
8.450
2.604
0.200
-1.609
CraigLieb
8.470
2.775
0.170
-1.772
Hernalt
7.929
3.430
0.141
-1.956
Jimmy Murdok
9.290
2.716
0.120
-2.120
Tass
8.614
3.120
0.117
-2.149
toruonu
9.370
3.468
0.110
-2.207
averagespacejoe
8.351
2.786
0.103
-2.272
arachnitect
8.330
2.793
0.100
-2.303
skybum
8.750
2.906
0.090
-2.408
schaban
8.900
3.231
0.080
-2.526
MEAN
9.722
3.591
0.075
-2.588
sdsds
9.530
3.818
0.070
-2.659
topsphere
10.170
3.373
0.060
-2.813
NaN
9.880
2.997
0.051
-2.972
nadreck
10.980
3.659
0.050
-2.991
Billium
11.250
3.209
0.050
-2.996
cscott
10.892
3.246
0.045
-3.101
Lar
11.951
3.654
0.040
-3.218
MikeAtkinson
11.773
3.605
0.040
-3.219
SINGLE-NUMBER POLL
10.826
3.122
0.036
-3.323
aameise
12.003
3.518
0.035
-3.360
Proponent
11.545
3.398
0.028
-3.576
mheney
11.660
2.815
0.020
-3.912
saliva_sweet
4.000
0.000
0.000
-Inf
The winner is Garrett, who assigned a likelihood of 20.0% to seven launches. Not only is his likelihood highest, but the entropy of his likelihood distribution is one of the lowest, meaning that he made a relatively precise prediction. I'm one of the worst performers, having assigned a likelihood of just 2.8% to seven launches.
It's interesting that despite having just 22 participants, this poll assigned a much higher mean likelihood (7.5%) to seven launches than did the single-vote poll (3.6%), which had 667 participants.
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NathanSyn
,
saliva_sweet
,
deruch
and
2 others like this
sdsds
Senior Member
Posts: 6658
“With peace and hope for all mankind.”
Seattle
Liked: 1618
Likes Given: 1544
Re: Likelihood Distribution of Number of SpaceX Launches in 2015
«
Reply #26 on:
01/02/2016 08:06 am »
A mere "thumbs up" doesn't adequately convey how much I like this! Thanks for putting it together!
I note that the distribution with mean closest to the actual seven launches was that offered by Hernalt. Though that's not a victory, it deserves recognition. (On a personal note, my guess was about as "middle of the road" as possible, with 10 guesses "better" and 11 guesses "worse" than mine.)
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— 𝐬𝐝𝐒𝐝𝐬 —
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