Wednesday, July 07, 2010
Probabilistic Design of Water Infrastructure
I am writing an article on statistical methods to optimize water infrastructure design. The idea is very simple: normally we use "design population", "design demand" etc. but reality is not like that but probabilistic. There is a certain probability that the demand in 2030 will be this and another probability that it will be that. Infrastructure such as pumping stations, tanks, etc. comes in discrete capacities, that is, a tank for 2000 cu me may cost 10,000 dollars, and the next one is 5000 cu m and will sell for 30,000 dollars. If my design number indicates 6000 cu m I will order the more expensive tank. But using statistics, it may well be that 5000 cu m will be sufficient in 99% of the time and the 1% may be less than the statistical error. Or let them have no water for five minutes once every ten years. Another way of looking at this is that the 6000 cu m tank will be needed only when 3000 independent consumers open their faucets at the same time - what is the probability of this happening in my lifetime or better, till the next elections?
Another issue that should be dealt with probabilitically is the number of cubicles in the toilet. What is the probability that all the cubicles are occupied and how much time has to wait the next person to access one? It is a gaussian distribution thingie, but no one ever calculates anything. We just look the Ministry of Health table and adopt the number written there. Space, in many cases, is critical, and my Clients are desperate to minimize the number of cubicles, but you cannot negotiate with a table. Which was designed with the worst case ihn mind, such as a sport stadium where everybody runs to releave himself during the half time, and they have multiplied this worst case scenario by a security factor of 100%, so no one - ever - will come to protest to the Ministry that they approved a poorly designed project.
You know, Israelis are in the lookout for these cases so they can accuse the authorities of being corrupt or for some other evil intension, like putting the interest of the rich (builders) before the interest of the defenseless public. I am aware that if I submit a design that has less than the number of cubicles ordered by the official table and try to defend my position by probabilistic calculation, the bureaucrats will hate me forever, for asking them to think and for committing the most imperdonable sin of forcing them to take a decision.