Number of simulations needed. A paper published in Fire Technology (Vol. 56, 2020) analyzed how many simulations are required to accurately represent the modelled scenario when using stochastic egress models. Engineers are mostly interested in a representative Total Evacuation Time (TET), and the average total egress curve (AC) has been suggested as an improved measure. Therefore, the paper presented a novel application of bootstrapping, functional analysis measures (FAMs), and a bisection algorithm to derive three FAM-based confidence intervals representing the precision of the AC for simulations sample sizes between 10 and 4000. The 90% confidence interval of the mean values of the bootstrap sample was (117.1, 176.0) and the 90% confidence interval of the mean values of conventional calculation was (108.3, 170.8).

a. What confidence coefficient was used to generate the confidence intervals?

b. Give a practical interpretation the 90% confidence intervals. Use the phrase “90% confident” in your answer.

c. When you say you are “90% confident,” what do you mean?

d. If you want to reduce the width of each confidence interval, should you use a smaller or larger confidence coefficient? Explain.