When modelling risks, usually a triangular distribution based on three time estimates (optimistic, likehood and pessimistic time estimates - a, c, and b respectively) is used to evaluate the planning task duration.
Once task distributions are known, a Monte Carlo algorithm generates an array of possible outcomes, resulting in better schedule overview when compared with a fully deterministic approach.
Because the triangular Probability Density Function (PDF) is zero in a and b, an appealing method to solve for a and b is based on using percentile estimates. As a matter of fact, it is possible to define a triangular PDF by specifying a lower percentile ap such that a < ap <= c <= br < b (see here: percentile). This approach avoids to specify the lower and upper extremes a and b that by definition have a zero likelihood of occurrence.
The value of p = 0.1 (then q = 1 - 0.1 = 0.9) specified in percentile is one of the possible value we can set for p. For instance I could choose p = 0.15 (q = 0.85). The point is that this value affect significantly the results of the Monte Carlo simulation, even when a large number of iteration (30000) is used for simulating risks. In other words, risk analysis result sensitivity to percentile is high.
So, is there a rule of thumb and/or mathematical constraints I have to account for to set the percentile value?