probability and project management, continued

one question that immediately arises with probabilistic scheduling: how do i define pdfs/cdfs for individual tasks? network combinations of tasks are straightforward from there, and the averaging that happens probably makes the small-scale choices less important as long as there aren't bias errors. it seems popular to use the beta or triangular distributions with upper and lower bounds and a most likely time. the bounds are important, i think, because no task will have <= 0 time and eventually i will need to quit. to make this work with the idea in the last post about a success/failure + time joint pdf, i would need pdfs for both success and failure and a probability of success. there are constraints, though; the success and failure marginal pdfs should have the same upper bound. (once success is no longer possible, failure is guaranteed.) they could have different lower bounds. (the time required to realize something is impossible could be more or less than the minimum time to succeed.) now here's an interesting question: will my pdfs tell me to try an alternate task before i've failed the first one? in other words, can a marginal pdf conditioned on a minimum time (the time i've already spent on it) tell me that my chance of success is so low that i might as well try the next approach? this could very well happen if the most likely time given success is shorter than the most likely time given failure, and i reach the time in between the two without finishing. hmmm, this could be useful. but it also makes the order optimization more complicated if i need to assume that i will switch to the next alternate before failing. project management people have acknowledged the fact that it's hard for people to estimate probabilities in the absence of data. i could at least evaluate my estimation in hindsight, however, by looking at the distribution of the estimated cdf value at the realized time. under the null hypothesis of always getting the right distribution, this empirical distro should be uniform on [0,1].