Bad weather causes delay and additional cost. An analysis shows that certain bad weather conditions occur 8% of the time and cause work to stop. The range of bad weather weeks per annum ranges :- Min=2, Mode=7 and Max=9.
The chance of bad weather is 100% quantum is the issue. Can you have a risk with aP()=1?
How do you quantify the P() of a storm that is 1 in 50 or 1 in 100 years in probability terms?
It depends on how you define "bad weather", which includes a specification of how bad for how long. You appear to have three different definitions in mind:
1. A "bad weather week", which is an event that stops work. (This happens in roughly 8% of weeks; or somewhere between 2 and 9 times a year).
2. A "bad weather year", which is a year containing at least one bad weather week. (the probability of a year being a bad weather year is presumably near 100%)
3. A "really bad year", which we dont have a deinition for (but we know that its probability is 1/50 or 1/100). Presumably it features a week with weather that is far worse than a mere "bad weather week".
The frequency versus number of bad weeks per year will follow a power curve. The binary "bad weather" is not enough information to say much more than that. The "analysis" needs to be redone and produce a dataset of weather weeks that can be sampled.
What do you mean by "8% of the time?" Is that 8 weeks out of a hundred? Hard to square with 2-9 weeks out of 52, or ~4-18 weeks out of a hundred. Are you saying that the bad weeks per annum parameters are min:2, mode:7, max:9, mean:4?
Your choice of min and max seems a bit naive. Are you saying that there is zero probability of a year with one or ten bad weeks?
Re second question: You have three ways to express this: As the probability of the event occuring within a particular time scale (.01 probability of occurence in any one year), or the expected number of events in a (longer) time scale, or preferably as a probability distribution plotting frequency against elapsed time (this is where I would sample the data used for the "analysis").