Re: [SystemSafety] Statistical Assessment of SW ......

From: Matthew Squair < >
Date: Sat, 24 Jan 2015 10:12:21 +1100


With apologies to Peter Bishop, I meant to send this to the group but selected the wrong damn button*.

Another non-trivial hardware problem is how to ensure a shared concept of time in a distributed system in the presence of clock drift. Said drift can lead to quite different responses to inputs from redundant identical components, based on their hitting a time gate at slightly different moments.

*Likelihood of operator error 1x10-3/D (WASH1400 study App III).

On Sat, Jan 24, 2015 at 1:50 AM, Peter Bishop <pgb_at_xxxxxx

> Determinism is tricky if you include hardware (especially embedded system
> hardware).
> One source of non-determinism is input measurement accuracy.
> Multiple "correct" responses are possible if a deterministic threshold
> (like trip or no-trip) relies on a real world input value.
>
> This can be a real problem when testing an embedded system.
>
> Peter Bishop
>
>
> RICQUE Bertrand (SAGEM DEFENSE SECURITE) wrote:
>
>> Does a deterministic software exist ?
>>
>> If it is intrinsically deterministic, does a deterministic execution
>> of this SW on a given hardware exist ?
>>
>> Bertrand Ricque Program Manager Optronics and Defence Division Sights
>> Program Mob : +33 6 87 47 84 64 Tel : +33 1 58 11 96 82
>> Bertrand.ricque_at_xxxxxx >>
>>
>> -----Original Message----- From:
>> systemsafety-bounces_at_xxxxxx >> [mailto:systemsafety-bounces_at_xxxxxx >> Behalf Of Peter Bernard Ladkin Sent: Friday, January 23, 2015 7:43 AM
>> To: systemsafety_at_xxxxxx >> [SystemSafety] Statistical Assessment of SW ......
>>
>> On 2015-01-21 14:15 , jean-louis Boulanger wrote:
>>
>>> For software it's not possible to have statistical evidence. the
>>> failure is 1 (yes the software have fault and failure appear)
>>>
>>
>> This argument came up again yesterday in a standards-committee
>> meeting. It is usually attributed to third party "engineers with whom
>> I work", because nobody quite seems to claim they hold the view
>> themselves when I'm in the room :-) ....
>>
>> So it might be worthwhile to adduce the proof - again. It's real
>> short.
>>
>> Suppose you have a piece of SW S which is deterministic. And S is
>> also not perfect, so it outputs right answers on some inputs and
>> wrong answers on others. And S reverts to an initial state with no
>> memory of its previous behavior each time it produces its output.
>>
>> Suppose the distribution of inputs to S has a stochastic character.
>> That is, the input I is a random variable. Then the output outS(I),
>> which is a function of the input I, also has stochastic character. A
>> deterministic transformation of a random variable is itself a random
>> variable.
>>
>> Let us transform outS(I) further, deterministically. Define CorrS(I)
>> = 1 if outS(I) is correct CorrS(I) = 0 if outS(I) is incorrect
>>
>> Then again CorrS(I) has also a stochastic nature and is a random
>> variable.
>>
>> Thus, if the input to a piece of SW has stochastic nature, then so
>> does the correctness behavior of the SW.
>>
>> QED.
>>
>> The only reasonable objection to this argument which I have heard is
>> to dispute whether inputs have a stochastic nature.
>>
>> So, say you build a railway locomotive control system. The piece of
>> track the locomotive runs on has a fixed architecture, so the
>> argument would run that the behavior of the locomotive is more or
>> less determined within certain parameters (whether signal X is red or
>> green) and does not have a stochastic nature. But various parameters
>> such as the condition of the track, the nature of the load on the
>> locomotive, and other environmental conditions such as wind speed and
>> weather (icy track, or dry track, and when icy where the ice is) make
>> it practically all but impossible to predict the inputs to the
>> control system. Besides, at design time the design does not involve
>> designing to the specific route the locomotive will run on. The
>> designer is ignorant of the application. So the inputs to the control
>> system as known at design time have a stochastic nature if you are a
>> Bayesian.
>>
>> I would like to remark here, again, on a couple of incoherences in
>> IEC 61508 and "derivative" standards.
>>
>> Something which executes a safety function must consist of both HW
>> and SW, because SW alone cannot take action. A HW-SW element which
>> executes a safety function is assigned a reliability goal, which is
>> mostly encapsulated in the SIL. These reliability goals are the
>> safety requirements. A reliability goal is expressed in terms of
>> probability of function failure per demand, or per unit time. Suppose
>> that the correct functioning of the HW-SW element E is functionally
>> dependent on the correct functioning of its SW S (which for most
>> actuators it is). The standard requires one demonstrates that the
>> reliability is attained (that the safety requirement is fulfilled).
>>
>> How this is actually done must be something like the following.
>>
>> We assume as above that the element E deterministically transforms
>> its inputs. We define the function CorrE as above. Given a
>> distribution of inputs Distr(I), then the probability that E
>> functions correctly is given by (Integral over Distr(I) of the
>> function CorrE(I)) divided by (Integral over Distr(I) of the constant
>> 1).
>>
>> Notice that the probability of correct functioning, the safety
>> requirement as laid down by IEC 61508, is dependent on Distr(I).
>> Change Distr(I) and one can usually expect the probability to change.
>> (For example, let Distr(I) be the Dirac Delta function on one
>> incorrect input. Then the probability that E functions correctly is
>> 0.)
>>
>> Yet in IEC 61508, and everywhere else, Distr(I) is not mentioned. Not
>> once.
>>
>> This is incoherent.
>>
>> One could fix it, maybe, by just assuming the uniform distribution on
>> all inputs, by default. Or the normal distribution. There may be
>> reasons for this, but it is worth pointing out that Distr(I) in real
>> applications is almost never uniform or normal. If there is a
>> distribution D for which it can be argued that the real-world input
>> distribution "almost always approximates D" then one could choose D
>> as the default instead.
>>
>> The second incoherence is as follows. If the SW does not attain the
>> safety requirement, then E does not attain the safety requirement,
>> under a certain plausible assumption, namely that if CorrS(I) = 0,
>> then CorrE(I) is almost always 0. (That is, the HW may sometimes
>> fortuitously compensate for incorrect SW behavior, but mostly not.)
>> Then in order for E to fulfil the safety requirement, it must be the
>> case that
>>
>> (Integral over Distr(I) of the function CorrS(I)) divided by
>> (Integral over Distr(I) of the constant 1) GEQ (Integral over
>> Distr(I) of the function CorrE(I)) divided by (Integral over Distr(I)
>> of the constant 1)- epsilon
>>
>> (epsilon is there to instantiate the "almost" part of the
>> assumption).
>>
>> So, since the safety requirement on E has a probabilistic calculation
>> as a component, so must the inherited safety requirement on S.
>>
>> Yet there is no requirement in IEC 61508 to substantiate that
>> inherited safety requirement on S. The only condition on software
>> safety requirements is the techniques which are recommended to be
>> used during development of S.
>>
>> In particular, if you don't think that the execution of SW can have a
>> stochastic nature, such as Jean-Louis, you are thereby committed to
>> the view that IEC 61508 and its derivates are inherently incoherent.
>> It must be a difficult world to live in ......
>>
>> PBL
>>
>>
>> Prof. Peter Bernard Ladkin, Faculty of Technology, University of
>> Bielefeld, 33594 Bielefeld, Germany Je suis Charlie Tel+msg +49
>> (0)521 880 7319 www.rvs.uni-bielefeld.de
>>
>>
>>
>>
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> --
>
> Peter Bishop
> Chief Scientist
> Adelard LLP
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-- 
*Matthew Squair*
MIEAust CPEng

Mob: +61 488770655
Email: MattSquair_at_xxxxxx
Website: www.criticaluncertainties.com <http://criticaluncertainties.com/>



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Received on Sat Jan 24 2015 - 00:12:33 CET

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