Probability of occurrence

I need your help, and I hope I can explain it correctly
I have a very important piece of equipment that has a high risk of failure if an event occurs
The failure will occur if I have a power failure (a once a year probability) and 1 valve needs to fail. I don’t know the probability of the valve failing (supplier of valve has indicated that it is very reliable, hence conservatively maybe two failures a year)
Remembering that the high risk event will occur only if I have a power failure and a valve failure I don’t know whether I should test for valve failure daily, weekly or monthly

your help is much appreciated


Active Member
sounds like valve failure is 2/365, power is 1/365 probability of occurring per day? If the events are independant (ie unrelated, no common causes or relationships), then the chance that both occur on a given day is 2/36t5 * 1/365 = 2/365^2.

suppose you go x days, then the chance of having high risk event on any day is 1 - (1 - (2/365^2) )^x. notice this goes to 1 as x gets big, ie it happens eventually.

Now the real question is what is the cost of the 'high risk event' compared to the cost of checking a valve?