[aadl]: Question about error model events distribution

[Viet Yen Nguyen]

Hi Denis,

I see this question has not yet been answered publicly. Even though I do
not have the current version of the AADL Error Annex in front of me, allow
me to explain it in terms of probability theory fundamentals.

As you state, a fixed distribution means that you'll have discrete
distribution over Booleans: a sample space of two outcomes: occurred and
not occurred. The Poisson distribution is a discrete distribution over
integers. It has an infinite discrete sample space: 0, 1, 2, ... Let us
translate that to practical terms. The sample 1 means that the error event
occurs 1 time (within the timeframe according to the \lambda parameter of
the Poisson distribution). The sample 100 means that the error event occurs
100 times. Given the \lambda parameter, the Poisson distribution assigns a
probability to that, e.g. the probability that the error event occurs 100
times.

Another interesting distribution is the exponential one. It's continuous
and spawns a probability distribution over the waiting time before the
error event happened. For example, the probability that you're 100 time
units in the OK state before the error event happens.

Viet Yen



On Mon, Oct 13, 2014 at 2:30 PM, Denis Buzdalov <buzdalov at ispras.ru> wrote:

> Dear all,
>
> We have a question related to the events occurrence distribution
> setting in the EMV2.
>
> We are talking about events occurrence and that's why the sample space
> of a probability space is a set of two elements, let's designate them as
> "OCCURED" and "NOT_OCCURED".
>
> If we are talking about fixed distribution defined on this sample
> space, everything is OK -- the only probability parameter (let's call
> it 'p') means that the probability mass of the event "OCCURED" is 'p'
> and the probability mass of the event "NOT_OCCURED" is '1 - p'.
>
> The occurrence distribution property in EMV2 allows to set difference
> probability distributions, not only the "fixed". One of possible
> variants is the Poisson distribution.
>
> The Poisson distribution can be used only with sample space of the set
> of natural numbers (i.e. the Poisson distribution say the probability
> of occurrence of some natural number). But events, as I said before, use
> the sample space containing only two values ("OCCURED", "NOT_OCCURED").
> That's why we have a conflict.
>
> So, the question is what is the meaning of occurrence distribution
> property setting applied to some event in case when the distribution is
> set to Poisson? What are probabilities of "OCCURED" and "NOT_OCCURED"
> sample space elements in this case?
>
> --
> Denis Buzdalov, Sergey Zelenov
> Software Engineering Department, ISPRAS
>
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