Schedule Risk Analysis: Measuring the time sensitivity of an activity

Submitted by Mario Vanhoucke on Fri, 12/02/2011 - 11:33

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, as described in “Bottom-up project control: Setting action thresholds using schedule risk analysis”.

In this article, four activity sensitivity measures will be discussed, which can be summarized as follows:

Criticality Index (CI): Measures the probability that an activity is on the critical path.
Significance Index (SI): Measures the relative importance of an activity.
Schedule Sensitivity Index (SSI): Measures the relative importance of an activity taking the CI into account.
Cruciality Index (CRI): Measures the correlation between the activity duration and the total project duration.

Criticality Index (CI)

The Criticality Index measures the probability that an activity lies on the critical path. It is a simple measure expressed as a percentage denoting the likelihood of being critical. Although the CI has been used throughout various studies and implemented in many software tools, the CI often fails in adequately measuring the project risk. The main drawback of the CI is that its focus is restricted to measuring probability, which does not necessarily mean that high CI activities have a high impact on the total project duration (e.g. think of an activity with a very low duration always lying on the critical path, but with a low impact on the total project duration due to its negligible duration). More information and an example project simulation run can be found in “Measuring time sensitivity in a project: the criticality index”.

Significance Index (SI)

In order to reflect the relative importance between project activities, the Sensitivity Index of a project activity can be calculated as follows:

SI = E{(ActivityDuration * ProjectDuration) / ((ActivityDuration + ActivitySlack) * E(ProjectDuration))}

with E(x) denoting the expected value of x. The SI has been defined as a partial answer to the criticism on the CI. Rather than expressing an activity's criticality by the probability concept, the SI aims at exposing the significance of individual activities on the total project duration. In some examples, the SI seems to provide more acceptable information about the relative importance of activities. Despite this, there are still examples where counter-intuitive results are reported. More information and an example project simulation run can be found in “Measuring time sensitivity in a project: the significance index”.

Schedule Sensitivity Index (SSI)

The Project Management Body Of Knowledge (PMBOK) mentions quantitative risk analysis as one of many risk assessment methods, and proposes to combine the activity duration and project duration standard deviations (StDevActivityDuration and StDevProjectDuration) with the CI. The Schedule Sensitivity Index is calculated as follows:

SSI = (StDevActivityDuration * CI) / StDevProjectDuration

More information and an example project simulation run can be found in “Measuring time sensitivity in a project: the schedule sensitivity index”.

Cruciality Index (CRI)

Another measure to calculate the duration sensitivity of individual activities is given by the correlation between the activity duration and the total project duration and can be calculated as follows:

CRI = |correlation(ActivityDuration, ProjectDuration)|

This measure reflects the relative importance of an activity in a more intuitive way and calculates the portion of total project duration uncertainty that can be explained by the uncertainty of an activity.

Pearson's product-moment CRI(r) is a traditional measure of the degree of linear relationship between two variables. The correlation is 1 in the case of a clear positive linear relationship, −1 in the case of a clear negative linear relationship, and some value in between in all other cases, indicating the degree of linear dependence between the activity duration and the total project duration. The closer the coefficient is to either −1 or 1, the stronger the correlation between these two variables. When the absolute value is taken, the CRI(r) lies between 0 and 1.

However, the relation between an activity duration and the total project duration often follows a non-linear relation. Therefore, non-linear correlation measures such as the Spearman rank correlation coefficient or Kendall's tau measure can also be calculated. These two correlation measures can be calculated as follows:

Spearman's rank correlation CRI(ρ) (rho) assumes that the values for the variables (i.e. activity durations and project durations) are converted to ranks, followed by the calculation of the difference between the ranks of each observation of the two variables. The measure is a so-called non-parametric measure to deal with situations where the strict statistical assumptions of the parametric CRI(r) measure are not met. The CRI(ρ) measure has a similar meaning to the CRI(r) measure, i.e. -1 ≤ CRI(ρ) ≤ 1 or, when the absolute value is taken, 0 ≤ CRI(ρ) ≤ 1.
Kendall's tau rank correlation CRI(τ) (tau) index measures the degree of correspondence between two rankings and assesses the significance of this correspondence. This non-parametric measure has a similar meaning to the CRI(r) measure, i.e. -1 ≤ CRI(τ) ≤ 1 or, when the absolute value is taken, 0 ≤ CRI(τ) ≤ 1.

More information and an example project simulation run can be found in three articles on the cruciality index, “Measuring time sensitivity in a project: the cruciality index (Pearson’s product-moment)”, “Measuring time sensitivity in a project: the cruciality index (Spearman’s rank correlation)” and “Measuring time sensitivity in a project: the cruciality index (Kendall’s tau rank correlation)”. Note that these three versions of the cruciality index can also be used to measure the sensitivity of the cost of each activity.

PM Knowledge Center

Schedule Risk Analysis: Measuring the time sensitivity of an activity