# Schedule Risk Analysis: Measuring the time sensitivity of an activity

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)**

**Significance Index (SI)**

**Schedule Sensitivity Index (SSI)**

**Cruciality Index (CRI)**

- 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.

- 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.

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