1. SOME MORE STATISTICAL ANALYSIS OF TRAINING DATA
CERN, 13th August 2015
QBT meeting
SOME MORE STATISTICAL ANALYSIS OF TRAINING DATA
E. Todesco, P. Hagen
CERN, Geneva Switzerland
Based on the HC data of 2015 and 2008
Thanks to MP3 teams

2. CONTENTS Reminder of available data Some special analysis
56 case: training in 2008 vs 2015 – did we see some improvement?
Which are the slow trainers?
Secondary quenches: do they reduce the training?
Is the 3000 series training behaviour uniform?

3. DATA REMINDER: SECTORS
Sectors are not homogeneous in terms of installed magnets

4. DATA REMINDER: TRAINING
Sectors are not homogeneous in terms of performance
For 3000 series, 45 much worse, and 78 much better
For 2000 series, 78 much worse

5. DID SECTOR 56 GET BETTER OR WORSE WITH TIME ?
Sector 5-6 powered twice to 6.5 TeV A
N= series magnets
In 2008 it took 24 quenches to reach A
Probability of quench in 2008 is p2008=24/84=30%
In 2015 it took 17 quenches to reach A
Probability of quench in 2015 is p2015=17/84=20%
Binomial distribution, taking two sigma we have
2008 quenches: 24±8
2015 quenches: 17±7
Data are compatible with the same distribution (no improvement, no degradation)

6. WHICH MAGNETS ARE BAD IN 56?
Two extreme situations can be imagined:
In 56 there are some bad magnets, always quenching, and other good magnets, never quenching
In this case, all magnet quenching in 2008 will quench in 2015
In 56 all magnets are belonging to the same distribution, with a probability p of quenching
In this case, the probability of having magnet quenching in 2008 and in 2015 will be p2(0.25)2=6%
So it is enough to count how many magnet quenched both in 2008 and in 2015
3 magnets quenched in 2008 and 2015:
3358, 3330 and 3336 out of 84, ie 3%
So magnets in 56 look equally bad
Do not replace what quenched since next time it will be another one

7. SECONDARY QUENCHES IMPROVE TRAINING?
We considered secondary quenches on neighbour magnets at currents larger than 6 kA
Are these secondary quenches reducing the probability of quench?
Example sector 45: we had 20 secondary quenches above 6 kA – probability of quenching 3000 series in this sector is 74%, so in absence of improvement we expect 15 quenches among these magnets – but we see only 6
YES there is improvement – probability of quench reduced by 65%

8. SECONDARY QUENCHES IMPROVE TRAINING?
If we place the cut at 7 kA, the improvement is larger
42 secondary quenches, only one magnet of these 42 quenched after the secondary training, against 14±6 expected

9. DOES TRAINING OF ONE APERTURE IMPROVES THE TRAINING IN THE OTHER ONE?
According to the previous result, we would conclude that quenching one aperture trains the other one
MP3 data are missing the aperture, so in case of double quench we do not know if it is the same or a second one
This can be recovered from timber, and will be done soon
For the moment, we see double quench in a percentage of apertures compatible with the product of probabilities so
Either the same aperture is quenching (weak magnet, out of statistics)
Either different apertures are quenching and the whole magnet is weak
Either the training of one aperture does not train the second one, that would be against previous result
It is important to record the aperture in the future MP3 data

10. UNIFORMITY OF 3000 SERIES
There is a clear indication of a non uniform production of 3000 series
See Gerard plot with a binning of 10
With a binomial, p=0.5, and N=10 the sigma over the probability is so with 2 sigma 0.8 and 0.2 are at the limit of significancy

11. 2015 DATA Binning of 104: Binning of 52:
Clear evidence of a good start for the first 100 magnets (p0.1 quenches per magnet), and then jump to 0.5, reduced to 0.3
Binning of 52:
After 100, transition towards worst part of production in two steps (p=0.3 and then p=0.65)
Then compatible with p=0.3

12. 2015 DATA Binning of 26: We have 3 magnets:
Recovery of performance from 3175, plus a final bad batch
We have 3 magnets:
3096 and 3100 clearly belong to the good batch
3409 is in the final bad batch, but not the worse ( ) that mostly went in 45