# Measuring time sensitivity in a project: The schedule sensitivity index

Schedule Risk Analysis (SRA) is a simple yet effective technique to connect the risk information of project activities to the baseline schedule, in order to provide sensitivity information of individual project activities to assess the potential impact of uncertainty on the final project duration. A traditional schedule risk analysis requires four steps, as described in “Schedule Risk Analysis: How to measure your baseline schedule’s sensitivity?”, to report activity sensitivity measures that evaluate each activity’s time estimate on a scale of risk. These sensitivity measures can be used by the project manager to distinguish between risky and non-risky activities in order to better focus on those activities that might have an impact on the overall project objective.

In this article, the Schedule Sensitivity Index (SSI) calculations are illustrated on a fictitious example project network with 8 activities, as displayed in figure 1. The number above each node is the baseline duration estimate (in days).

Figure 1: A fictitious example project network

The baseline schedule has a planned duration PD = 90 days and the critical path is equal to the activity sequence 1 - 2 - 5 - 8. However, the baseline schedule is only an estimate of the real project duration and hence, the real project duration and the critical path might differ from the baseline schedule estimates. Consequently, the critical path is a black-and-white view on the critical parts of a project, and should be refined to capture more detailed sensitivity information.

Schedule sensitivity index

The Project Management Body Of Knowledge (PMBOK) proposes to combine the activity duration and project duration standard deviations with the Criticality Index. In this article, the following abbreviations will be used:

StDevAD: The standard deviation of the activity duration
AvgSD: Average simulated project duration
StDevSD: The standard deviation of the simulated activity duration
CI: Criticality index

The Schedule Sensitivity Index can be calculated as follows:

SSI = (StDevAD * CI) / StDevSD

Table 1 displays 10 simulation runs where each activity has a certain duration which might differ from the original baseline duration estimate given in figure 1. The simulated project duration (SD) for activities 1 to 8 per simulation run is also given. Each simulation run reflects a possible real project progress scenario where unexpected changes in the activity estimates might occur.

Table 1: 10 simulation runs with random activity durations
 1 2 3 4 5 6 7 8 SD Run 1 4 12 1 4 5 4 7 8 29 Run 2 22 23 14 5 28 26 5 29 102 Run 3 25 38 12 15 24 20 13 22 109 Run 4 25 25 15 13 25 25 13 10 88 Run 5 21 42 12 7 30 21 14 23 116 Run 6 28 44 7 9 15 20 10 22 109 Run 7 19 21 14 13 23 24 14 28 99 Run 8 12 36 14 9 19 17 7 24 91 Run 9 28 35 7 12 28 27 13 28 119 Run 10 27 44 6 5 30 10 11 28 129

Based on the simulation runs, the schedule sensitivity index can be calculated with the intermediate calculations illustrated in table 2 for activity 2 of figure 1. In this example, the values for (AD - AvgAD) and (AD - AvgAD)2  are given for activity 2 with AvgAD = E(AD) = 32. Likewise, the SD - AvgSD and (SD - AvgSD)2 are displayed with AvgSD or E(SD) the average or expected value of the SD column of table 1, i.e. E(SD) = 99.1.

Based on the values in table 2, the standard deviations for the activity duration and project duration can be calculated as follows.

• StDevAD = 11.06 and is equal to the square root of the sum of the (AD - AvgAD)2 column of table 2 divided by 9.
• StDevSD = 27.65 and is equal to the square root of the sum of the (SD - AvgSD)2 column of table 2 divided by 9.
Note the division by 9 means the sample standard deviation is calculated and not the population standard deviation. For more information, the reader is referred to any introductory statistical book. The criticality index of activity 2 is equal to CI = 0.8, as illustrated in “Measuring time sensitivity in a project: the criticality index”, and consequently, the schedule sensitivity index is equal to:

SSI = 11.06 * 0.8 / 27.65 = 0.32.

Table 2: Intermediate calculations for the SSI of activity 2
 AD - AvgAD (AD - AvgAD)2 SD - AvgSD (SD - AvgSD)2 Run 1 -20 400 -70.1 4,914.01 Run 2 -9 81 2.9 8.41 Run 3 6 36 9.9 98.01 Run 4 -7 49 -11.1 123.21 Run 5 10 100 16.9 285.61 Run 6 12 144 9.9 98.01 Run 7 -11 121 -0.1 0.01 Run 8 4 16 -8.1 65.61 Run 9 3 9 19.9 396.01 Run 10 12 144 29.9 894.01

Although activity 2 lies on the critical path in the baseline schedule, the schedule sensitivity index is lower than 1. Figure 2 shows the SSI values for all project activities, ranging between 0% and 32%. More precisely, the values are equal to 0.28, 0.32, 0.03, 0.00, 0.23, 0.05, 0.02 and 0.27 for activities 1 to 8. Obviously, a schedule risk analysis should be done with care for the following two reasons: (1) the input distributions of the activity duration should reflect reality, and (2) the number of simulation runs should exceed 10 to provide more reliable results.

Figure 2: The sensitivity index values for the 8 activities after 10 simulation runs

The graph of figure 2 can be used to set action thresholds that make a distinction between sensitive and insensitive activities to better steer the project control process during project progress. More information can be found in “Bottom-up project control: Setting action thresholds using schedule risk analysis”. Apart from the schedule sensitivity index, other time sensitivity measures can also be calculated for the same simulation runs, as discussed in “Schedule Risk Analysis: Measuring the time sensitivity of an activity”.