Assignment: You are asked by the project manager to calculate an estimate pouring the foundation of an office building. Realistically, it should take four days since that is what your company routinel
9.4 Duration Estimation 309 of time (duration) it would take to place the steel girders needed to frame the bridge. We expect that the duration for the framing task will take six days; however, a number of factors could change that duration estimate. We could, for example, experience uncommonly good weather and have no technical delays, allowing us to finish the framing work in only four days. On the other hand, we could have terrible weather, experience delivery delays for needed materials, and lose time in labo\�r disputes, all leading to a pessimistic estimate of 14 days. This example\� demonstrates the asymmetri- cal nature of duration estimates; while our most likely duration is 6 days, the range can vary from 4 to 14 days to complete the task.The optimistic and pessimistic duration values essentially serve as upper and lower bounds for the distribution range. Figure 9.15 illustrates a beta distribution with the values m (most likely duration), a (most optimistic duration), and b (most pessimistic duration) identified. Two assumptions are used to convert the values of m, a, and b into estimates of the expected time (TE) and variance (s 2) of the duration for the activity. One important assumption is that s, the standard deviation of the duration required to complete the task, equals one-sixth of the range for reasonably possible time requirements. The variance for an activity duration estimate is given by the formula: s2= [(b -a)> 6] 2 The logic for this assumption is based on the understanding that to achi\�eve a probability distribution with a 99% confidence interval, observations should lie within three standard deviations of the mean in either direction. A spread of six standard deviations from tail to tail in the probability distribution, then, accounts for 99.7% of the possible activity duration alternatives.\� Because optimistic and pessimistic times are not symmetrical about the mean, the second assumption refers to the shape of the probability distribution. Again, the beta, or asymmetrical, dis - tribution better represents the distribution of possible alternative expected duration times (TE) for estimating activities. The beta distribution suggests that the calculati\�on for deriving TE is shown as: TE =(a +4m +b)> 6 where TE = estimated time for activity a = most optimistic time to complete the activity m = most likely time to complete the activity, (the mode of the distribution) b = most pessimistic time to complete the activity Beta distribution Elapsed time 0 m ab Figure 9.15 Asymmetrical (Beta) Distribution for Activity Duration estimation f(x) x Shaded area = 1– –Z 1– /2 Z1– /2 Figure 9.14 Symmetrical (Normal) Distribution for Activity Duration estimation
