Post date: Feb 23, 2014 9:16:13 PM
Matthias:
Greetings. I'm really sorry that you aren't going to be in Liverpool. It looks like I will finally meet Frank. Unless I can't attend or something....
I'm here at UTC with Sébastien and Mohamed Sallak, and we were talking a bit about your ISIPTA paper with Simon Blake and the possibility of relaxing the dependencies among components using Fréchet inequalities.
Mohamed claims that reliability engineers mostly assume their systems are "coherent", by which he means that the reliability is surely a monotone non-decreasing function of each component's reliability. This means of course that the system reliability (assuming independence among components) is pretty easy to compute in practice even if there are lots of scary repeated variables in the expressions. Much easier than I'd assumed.
It must be similarly easy to handle the Fréchet case too. The Frank-Nelsen-Sklar theorem applies in the multivariate case whenever the function is monotone in each variable, right? In some sense, the multivariate reliability function will be as simple as the bivariate function of addition. I think one of the papers by those Belgium economists pointed this out. Not sure how much of a pain it would be to actually make calculation though.
Are you familiar with this generalization? Have you thought about or tried to make such calculations? I know it sort of abandons the idea of the alpha-factor models, but it would clearly be a compelling solution to uncertainty about dependence, at least in cases where the results aren't too terribly wide.
I've not been frequenting our favorite restaurant, La Brasserie Parisienne, but every single time I walk by it I think of your giant dessert. I'm pretty sure the thought alone is making me fatter. That's right, it's the thinking about desserts that's doing it.
Cheers,
Scott
Bonjour Scott (CC also Frank),
Pouvez accepter mes excuses pour ze late respons...
On Wed, Feb 12, 2014 at 6:15 PM, SandP8 <sandp8@gmail.com> wrote:
> Greetings. I'm really sorry that you aren't going to be in Liverpool. It
> looks like I will finally meet Frank. Unless I can't attend or
> something....
>
> I'm here at UTC with Sébastien and Mohamed Sallak, and we were talking a bit
> about your ISIPTA paper with Simon Blake and the possibility of relaxing the
> dependencies among components using Fréchet inequalities.
>
> Mohamed claims that reliability engineers mostly assume their systems are
> "coherent", by which he means that the reliability is surely a monotone
> non-decreasing function of each component's reliability. This means of
> course that the system reliability (assuming independence among components)
> is pretty easy to compute in practice even if there are lots of scary
> repeated variables in the expressions. Much easier than I'd assumed.
>
> It must be similarly easy to handle the Fréchet case too. The
> Frank-Nelsen-Sklar theorem applies in the multivariate case whenever the
> function is monotone in each variable, right?
I'm not sure what you mean by "the function is monotone". The
cumulative distribution function is always monotone in all
arguments... ?
> In some sense, the
> multivariate reliability function will be as simple as the bivariate
> function of addition. I think one of the papers by those Belgium economists
> pointed this out. Not sure how much of a pain it would be to actually make
> calculation though.
>
> Are you familiar with this generalization? Have you thought about or tried
> to make such calculations? I know it sort of abandons the idea of the
> alpha-factor models, but it would clearly be a compelling solution to
> uncertainty about dependence, at least in cases where the results aren't too
> terribly wide.
No, we haven't tried to use copulas directly in this problem of
electrical network reliability, because it is much harder to segragate
the marginal failure model from the common failure information
(although Sebastien, Frank, and myself, have starting to think about
this in some more depth recently). The alpha factor is standard, does
a good job at segregation, and has a trivial imprecise extension... so
Simon and I took that. The theory behind it is in a joint paper with
Gero and Dana.
> I've not been frequenting our favorite restaurant, La Brasserie Parisienne,
> but every single time I walk by it I think of your giant dessert. I'm
> pretty sure the thought alone is making me fatter. That's right, it's the
> thinking about desserts that's doing it.
:-)
Salut,
Matthias Troffaes
To clarify one thing:
A system is coherent means indeed that there is no state of components such that,
if one (or more) more components fail, the system's functioning improves (the latter
is usually seen as a 0-1 variable, but not necessarily so).
I have seen quite some work on non-coherent systems, but I am quite sceptical
about it: I think that in such systems one typically does not provide enough detail
in the system state - indeed if one just uses a 0-1 variable then it can happen
(two failures can cancel each other out) but the real state would probably require
to include the info, as e.g. maintenance would be required.
Frank Coolen