Merge Bias and Schedule Underestimation
One of the most important reasons for performing a schedule risk analysis is that the overall program schedule duration may well be greater than the sum of the path durations for lower-level activities. This is so partly because of schedule uncertainty and schedule structure. A schedule’s structure has many points where parallel paths merge that can cause the schedule to lengthen. Merge points may include key program events such as preliminary design review, the beginning or ending of project phases, or product deliveries. The timing of these merge points is determined by the latest merging path. Thus, if a required element is delayed, the merge event will also be delayed. Because any merging path can be risky, any merging path can determine the timing of the merge event. Figure 36 gives an example of the schedule structure that illustrates the network of a simple schedule with a merge point at start-up and test.
Figure 36: A Simple Schedule as a Network Diagram
The added risk at merge points is called “merge bias.” As we discussed in Best Practice 2, risk at merge points is a concern because it is multiplicative. For example, suppose that a schedule risk analysis has determined that the two start-up and testing paths in figure 36 each has a 60 percent chance of finishing on time. The start-up paths are not necessarily a concern individually, but the success of the completion milestone is a concern. Its success is the probability of both paths completing on time—36 percent. In fact, given that each path has a 60 percent chance of success, the milestone will finish late in three of four scenarios: if the electrical test runs late but the plumbing test is on time (24 percent chance), if the electrical test is on time but the plumbing test runs late (24 percent chance), or if both the electrical and plumbing tests run late (16 percent chance).
The completion milestone is not likely to be on time even though each individual testing path is likely to complete on time. Moreover, the chance of success at a merge point decreases the more that paths converge. If a third test were added, say a furnace and air conditioning test, and its success is determined to be 60 percent also, the overall chance of success for the completion milestone would be 22 percent. Merge bias is one reason that the finish date of even a well-constructed schedule is likely to be later than scheduled. The bias is driven by a combination of risk on individual paths, the amount of free float before the milestone, and the number of merging paths at that milestone. Case study 14 provides an example of the potential effects of converging activities on scheduled activities.
The Coast Guard program office and Northrop Grumman officials said that schedule risk analysis (SRA) was not required for the National Security Cutter 3 (NSC 3) production contract and therefore it was not performed.
In the December 2010 program management review, only one risk was identified: “test or installation phase failure.” Given that the schedule in February 2011 had 3,920 remaining activities, one identified risk seemed improbable. For example, Northrop Grumman officials said that the critical end milestone they were most concerned about was a “preliminary delivery of NSC.” The critical milestone had 5 days of negative float and 57 converging predecessors. That is, the task was already 5 days behind schedule on the status date, and—compounding the risk of delay—had multiple converging activity paths that decreased the probability of meeting the planned milestone date.
The chance that the milestone will be accomplished on time decreases with every additional path leading up to the milestone. The more parallel paths that exist in the schedule, the greater the schedule risk is. A Monte Carlo SRA simulation could have helped identify the compound effect of parallel paths and could have quantified how much contingency reserve or margin was needed in the schedule to mitigate the risk.
Agency officials and Northrop Grumman said that a schedule risk analysis would be performed as part of the NSC 4 schedule.Because activity durations are uncertain, the probability distribution of the program’s total duration must be determined statistically, by combining the individual probability distributions of all paths according to their risks and the logical structure of the schedule. An accepted way to do this is to perform a Monte Carlo simulation of the schedule with uncertainty and risk applied.