Re: A more careful analysis of the roll-over errrors

Chris Orth (corth@budoe.bu.edu)
Wed, 13 Mar 1996 09:56:36 -0500 (EST)

>
> Hi Folks,
>
(recycling Chris W.'s greeting)

For continuity I will leave in the key points of Chris' Analysis

> Times between pulses in nano-seconds:
>
> 101125
> 14475
> 20665
> 28935
> 3545
> 49795
> 28060
> 300
> 38080
> 57965
> 35125
> 26540
> 24115
> 29290
> 41223
> 13700
> 73545
> 2415
> 14889
> 2997
>

(calculation removed)

> t_0 prob pulses separated > t0 ns
> 0 100%
> 30000 47%
> 330000 .03%
>
> So the chances of missing a roll-over word(going for 330uSec or longer
> with no data) is .03%. So how many roll-over misses do we expect to
> see?

> sample meets this requirement. This results in 393 events. Applying
> our .03% estimate we would expect .12 events.

Ok, if I follow correctly, you have calculated the chance for the time
separation of two consecutive radioactivities to be greater than a
rollover apart. The chance for a given WFD buffer that has a similar
radioactivity rate to miss a rollover is much bigger...

You quoted about 20 distinct times above. Assuming every pair is
independant (which as Chris mentioned is sort of a simple-minded
assumption), the the chance of NEVER missing a rollover in 20
radioactivities is about (.9997)^20. So the chance of missing a
rollover is 100*(1-.9997^20) = .6%.

So if this is typical it is kind of bad. It means that we lose close to
1% of the data for every 3:1 multiplexed channel.

>
> In fact we saw 3 events. This is an order of magnitude difference.
> I'm not sure what conclusions to draw given the assumptions I had to
> make but it seems plausible to try to look for other explanations.
> For example: could something 'bad' happen if one of the inputs has
> nothing plugged in to it?
>

I'm not interested in arguing orders of magnitude here... I think it is
worthwhile to look at what the corresponding rates are in other
channels. Bottom line is I want to know if we are going to have to worry
every time we want to turn a phototube off in macro ... fopr instance
5E03 has been off for about a week now, does this mean we may have also
lost 1% of the events on 5E01,5E05 and 5E07?

Chris