[aadl]: [AADL]: Question about error model events distribution

[Peter Feiler]

In the Error Model V2 Annex document we included the following distribution functions based on recommendations of Myron and other committee members. Full definitions for these functions can be found on Wikipedia.



DistributionFunction property type provides a predefined set of distribution functions.

*        Fixed represents a fixed distribution and takes a single parameter OccurrenceRate.

*        Poisson represents the Poisson distribution and takes a single parameter OccurrenceRate.

*        Exponential represents an exponential distribution and takes a single parameter OccurrenceRate.

*        Normal aka. Gauss represents a distribution with an explicitly specified MeanValue and StandardDeviation.

*        Weibull represents a shaped distribution with a ShapeParameter and a ScaleParameter.

*        Binominal represents a discrete distribution with a SuccessCount, a SampleCount, and a Probability parameter.
The distribution function is used in the property type

ProbabilityDistributionSpecification : type record (

        OccurrenceRate : aadlreal;

        MeanValue : aadlreal;

        StandardDeviation : aadlreal;

        ShapeParameter : aadlreal;

        ScaleParameter : aadlreal;

        SuccessCount : aadlreal;

        SampleCount : aadlreal;

        Probability : aadlreal;

        Distribution : EMV2::DistributionFunction;
);

It in turn is used the OccurrenceDistribution and DurationDistribution properties.

From: sae-aadl-users-bounces+phf=sei.cmu.edu at lists.sei.cmu.edu [mailto:sae-aadl-users-bounces+phf=sei.cmu.edu at lists.sei.cmu.edu] On Behalf Of Myron J Hecht
Sent: Wednesday, October 22, 2014 11:02 AM
To: Viet Yen Nguyen
Cc: sae-aadl-users-bounces+myron.j.hecht=aero.org at lists.sei.cmu.edu; Sergey Zelenov; sae-aadl-users
Subject: Re: [aadl]: [AADL]: Question about error model events distribution

Hello everyone

>Are you sure that it [Syntax of distributions] is formalized enough (e.g. in the standard text) to be used by instruments or formal analysis?

Probability distributions used in stochastic analysis of systems for reliability and safety are quite well defined.  Whether they are properly used is a function of the external calculation/simulation tool and the code that provides the interface from the EMV2 section of the AADL model to that tool.

Regards


Myron Hecht
Sr. Project Leader
The Aerospace Corporation
myron.hecht at aero.org<mailto:myron.hecht at aero.org>
310-336-3521



From:        Viet Yen Nguyen <nguyenvietyen at gmail.com<mailto:nguyenvietyen at gmail.com>>
To:        Denis Buzdalov <buzdalov at ispras.ru<mailto:buzdalov at ispras.ru>>,
Cc:        Sergey Zelenov <zelenov at ispras.ru<mailto:zelenov at ispras.ru>>, sae-aadl-users <sae-aadl-users at lists.sei.cmu.edu<mailto:sae-aadl-users at lists.sei.cmu.edu>>
Date:        10/22/2014 05:38 AM
Subject:        Re: [aadl]: Question about error model events distribution
Sent by:        sae-aadl-users-bounces+myron.j.hecht=aero.org at lists.sei.cmu.edu<mailto:sae-aadl-users-bounces+myron.j.hecht=aero.org at lists.sei.cmu.edu>
________________________________



Hi Denis,

1) Regarding time periods: the time period is implicit to the \lambda parameter. You of course have to make sure that all \lambda parameters in the model are based on the same time period. See also the definition of the Poisson distribution on Wikipedia.

2) Regarding the syntax and use of the distributions, I don't have a copy of the AADL Error Annex here at hand (the copy I used to have belonged to the my previous employer). I cannot therefore lookup and confirm for you whether the current text is formal enough on this. Perhaps somebody on the mailinglist who is more intimate with the AADL Error Annex can jump in here.

3) Theoretically, any probability distribution is oblivious towards its use. Its semantics are decoupled from the meaning of the random variable that is being probabilistically distributed. So far we've been taking about amount of occurrences, waiting times and decision answers as random variables. The choice of distribution for a random variable therefore depends on whether the distribution's characteristics match your intended semantics (i.e. the real world).

Viet Yen

On Wed, Oct 22, 2014 at 2:03 PM, Denis Buzdalov <buzdalov at ispras.ru<mailto:buzdalov at ispras.ru>> wrote:
Hi Viet Yen,

Thank you for your response. But, you know, I still have questions to
your answer.

> 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.

The first question is what period of time event occurrence is
considered? This distribution shows the probability of n occurrences of
event during what period of time?

> Given the \lambda parameter,
> the Poisson distribution assigns a probability to that, e.g. the
> probability that the error event occurs 100 times.

The second question is am I right that you mean that \lambda parameter
can be set through the 'ProbabilityValue' record part of the
'EMV2::OccurrenceDistribution' property value?

If the answer is 'yes', then another question rises: how would you
set parameters for multiple-parameterized distributions (like the Normal
distribution)?

If the answer to the second question is 'no' then I would ask how would
you set the \lambda parameter?

> 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.

This part of your answer makes me messed up completely.

Am I right that you mean that the semantics of distribution setting
depends completely on the distribution type: you have
- the probability of occurrence in one case,
- expected count of occurrences in the other case and
- expected time on the third case?

Are you sure that it is formalized enough (e.g. in the standard text)
to be used by instruments or formal analysis?

--
Denis Buzdalov
Software Engineering Department, ISPRAS
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