@ Umair Shahzad

Can you, please present the phenomena governing the mutual influence of the outages of the lines? What is the physical quantity measured in terms of the outage? Are this lines of the same type (like mass production line, street traffic, people leaving in emergency a stadium, electrical networks with shortages in supplied energy) or different (say, nr 1 counts outage of the product and line 2 couts the outage of garbage)? Why the gaussian pd is chosen for that model?

Obviously the first question is basic for any considerations.

Regards, Joachim

The load of the system is Gaussian, so it makes sense to make the line loading as Gaussian, Yes the lines are same type in every aspect. I want to see if there is a outage on Line 1, how does it effect the "loading" of line 2

I'm still not seeing any reason why the lines cooperate. Let me make my question a little bit more clear:

Assume we are producing product nr 1 on line nr 1 and product nr 2 on line nr 2. The lines are posed physically in different buildings. For some reasons their production is random, e.g due to the supply of the raw mterials and due to the quality of the service changing dayly. If the supply is independent, if the mashines are independent and if the teams are independent then no effect can be noted upon line 2 caused by the outage of line 1. But if, say, the supply is coming with common transportatian devices (like elevators, cars, walking people) then the influence is caused by common factor. In another model, say in the case when the result of the first line is the inlet for the second line, then we have influence of one outage onto the other. Now, one can easily imagine mutual influence, ec. This bothers me, which kind o impact i vlid, what is the reason you want to parametrize the impact, in which terms (e.g. via the correlation). . . ??

Respect, Joachim

I am talking about electrical lines in distribution system

Thus, what is the connection between the lines? Do they act simultaneously? Do the y supply the same receivers? what are the rules of switching - if any is performed - of the receivers/ senders? I am asking such perhaps stupid question, but I would like to show that there must be some reason that the lines influesce each other. There are some much more severe questions like this one: Are you considering a random gaussian process of the energy transfere? If yes, then is your unique goal the stationary outage. Even in this simplified question some idea of the processes of requests, potential ability of production of the energy and ventual damages of the lines and generators is required to have the model as close as possible to the reality.

PS. frankly I have no idea how such systems cooperate in case of low/high needs and in case of good, bad wether. Once in my past activity I habe met a problem where the lines were considered as dmagable with some low probability per 1km, per a year and per a wire, and the switches deviding the supply between different lines (in portions) had some reliability (probabilty of refusing proper connection per year per a piece. The problem was to calculate the probability of ensuring say 70 % of the needed energy. But there was no random process involved. In your problem the time dependence seens to be important, which I see from the continuity of the pd of the outage. I have now an imagination, that it is counted say per a day, in each day obtainable independently like in the sampling of simple trials in statistics. Then, surely, such quantity can be approximately modelled via continuous rv, the normal included.

Dear Sir, currently I am getting tired due to the end of day. I found you problem interesting, but still I really don't understnd you question.

Please elaborate it in some most imporatnt detailes, be it in non-physical terms - it does not matter. Let me suggest a type of formulations:

There is a structure with such and such elements. The proper activity is ensured in such and such cases, the elements have such and such probability to fail within unit of time, with the beginning of each unit of time the system is renewed, the probabilities of damages are independent. calculate the probability of the proper activity of the system (call it outage) and of each part separately. Obviously this is only a very very simplifiedexample of the way of posing the problem.

regards, Joachim

If you have two or more lines supplying a community, and some lines fall out, with an unchanged total load being redistributed on the surviving lines, I would guess the probability of these also failing due to overload is likely to increase. This happened in North America some years ago, triggering an avalanche of failures, https://en.wikipedia.org/wiki/Northeast_blackout_of_2003, and on many other occasions you can find described on the web.

But, as Joachim says, the details of this depend on how the whole system is configured, and f.i. protected against overloading.