Schedule Risk Analysis with Three-Point Duration Estimates
One way to capture schedule activity duration uncertainty is to collect various estimates from individuals and, perhaps, from a review of actual program performance. Table 2 shows a traditional approach with a three-point estimate applied directly to the activity durations for a section of the house construction schedule. The example shows threepoint estimates of remaining durations. In an actual program schedule risk analysis, these would be developed from in-depth interviews of persons who are knowledgeable in each of the WBS areas of the program.
Table 2: Estimated Durations for a Section of the House Schedule
| ID | Description | Minimum remaining duration | Most likely remaining duration | Maximum remaining duration |
|---|---|---|---|---|
| A1870 | Install drywall on walls and ceilings | 3 | 4 | 6 |
| A1880 | Inspect drywall screws | 1 | 1 | 2 |
| A1890 | Finish drywall (tape and mud) | 3 | 5 | 6 |
| A1900 | Install ceiling insulation | 1 | 1 | 2 |
| A1910 | Apply drywall texture | 2 | 3 | 4 |
| A1920 | Apply wall finishes (stain and paint) | 2 | 3 | 4 |
| A1930 | Install tile in bathroom and kitchen | 2 | 3 | 5 |
Source: GAO | GAO-16-89G
To model the risks in the simulation, the risks are represented as triangular distributions specified by the three-point estimates of the activity durations. In other words, for this example the 3-point estimates represent all the risk in the construction project. Distributions other than the triangular are traditionally available as well.34
Once the distributions have been established, a statistical simulation (typically a Monte Carlo simulation) uses random numbers to select specific durations from each activity probability distribution, and a new critical path and dates are calculated, including major milestone and program completion dates. The Monte Carlo simulation continues this random selection thousands of times, creating a new program duration estimate and critical path each time. The resulting frequency distribution displays the range of program completion dates along with the probabilities that activities will occur on these dates, as seen in figure 37.
Figure 37: The Cumulative Distribution of the House Construction Schedule
The figure shows that the expected completion date is February 25, not February 10, which is the date the deterministic schedule computed. The cumulative distribution shows that, in this instance, the likelihood is about 7 percent that the project will finish on February 10 or earlier, given the schedule and the risk ranges used for the durations. Moreover, a contractor planning for 70 percent certainty would promise completion on March 2, about a calendar month later than originally planned.
Three-point duration risk analyses, an acceptable method of conducting SRAs, are widely used. However, a disadvantage of using three-point duration ranges to represent all the risk in an analysis is that probability distributions for durations derived from risk interviews cannot be attributed to individual risk events. Interviewees may be combining any number of threats and opportunities in their single best case and worst case estimates. For example, a construction manager may suggest a worst-case scenario of 6 days to install drywall, as shown in table 2. However, the delay may be caused by lack of materials, poor labor productivity, poor weather, last-minute design changes, or some serial combination of all four risks. It is also possible that the SME has increased the pessimistic duration estimate to account for general uncertainty, in effect accounting for “unknown unknowns.” The result of the three-point duration SRA is a recommended amount of schedule contingency that covers both quantified risks and some level of uncertainty but gives no indication of which risks are most likely to affect the schedule.
For more information on developing probability distributions to model uncertainty, see chapter 14 in the GAO Cost Estimating and Assessment Guide, GAO-09-3SP.↩︎