# Re: Statistical errors in residual dose rates and activities and number of primaries/batches

From: Francesco Cerutti <Francesco.Cerutti_at_cern.ch>
Date: Tue, 14 Aug 2012 13:14:06 +0200

Dear Mina

> As I understand, the uncertainty we see in any given quantity in FLUKA
> is just the error in the mean of the quantity,
> where the mean is the average of the quantity as calculated from the
> result of the batches.
> So, the higher the fluctuations in a given quantity from run to run, the
> higher the variance and the error in the mean.

correct, as in the attached slide (note the last factor in the formula)

> I first came across this issue when doing Stefan's two-step process. From a study I did, I found out that the error in
> the dose rate, one week after EOB was on the order of 28% for 2 M primaries per run, 10 runs (20 M primaries total). I
> looked at the results of the individual runs and saw large fluctuations from run to run. This is what I saw for 10 runs
> (Dose rate in PSv/s):
>
> (766.4, 986.4, 1131.9, 1785.8, 4077.8, 224.2, 1143.6, 35.4, 1511.3, 939.9)
> So the result from combining all ten runs was 1260.3 +/- 28%.
>
> When I repeated the run for 5 M primaries/run, I saw smaller fluctuations:
> (907.8, 986.4, 749.2, 937.5, 587.2, 599.1, 726.8, 421.9, 985.3, 754.3)
> Average: 751.5 +/- 7.9%

The latter average seems to be indeed 765.6 (not 751.5)

> So obviously an improvement, which made me conclude that number of
> primaries per run does matter. Is this because the
> total number of primaries is increased in the 2nd case (5 M prim/run *10 runs = 50 M primaries)?

certainly yes!

> And that if I had run
> 5 M primaries/run but only 4 runs, I would have seen a similar error as in case 1?

In principle yes, but actually 4 runs are at the limit already indicated
by Alberto, making the error evaluation precarious

Best

Francesco

Received on Tue Aug 14 2012 - 22:31:53 CEST

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