indicator

true when each replication's response is 0 or 1 (the event happened or it did not), so that the estimate is a proportion and the average times the count is the number of replications in which the event happened. Feasibility is then tested with the exact (Clopper-Pearson) binomial bound instead of a normal-theory interval. That matters most when the event is rare: zero events in 30 replications has a sample variance of zero, and the normal-theory interval then has zero width and certifies the constraint with no evidence at all, while the exact bound at 95% is about 0.095.