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Quantitative risk analysis helps to numerically analyze the probability and impact of risks on project objectives. By performing quantitative risk analysis, the risk manager can present the risks with the most impact on achieving the project objectives to the project sponsor. (Reference: PMBOK Guide, 6th Edition, p. 423)

According to the PMI Risk Management Professional (PMI-RMP) Reference Materials, sensitivity analysis is a type of probabilistic analysis that determines how sensitive the results of the analysis are to uncertainties in input variables.Sensitivity analysis determines which uncertainty has the greatest potential for an impact on the project objectives, such as cost, schedule, scope, or quality1. In this case, the risk manager should use sensitivity analysis to facilitate the sponsor's ask, as it will help to identify and present the risks that have the most impact on achieving the project objectives.Sensitivity analysis can also show how the project objectives will vary with the changes in the input variables, such as the probability and impact of risks2.Sensitivity analysis can be performed using various tools and techniques, such as tornado diagrams, spider charts, or influence diagrams3.

The team is documenting all the checkpoints along the way that might indicate delays on critical deliverables, which is an example of risk triggers. Risk triggers are events or conditions that indicate a risk may be about to occur or has already occurred, helping the project team to monitor and respond to risks effectively.

Risk triggers are indicators or warning signs that a risk event is about to occur or has occurred. They help to monitor the status of risks and initiate risk responses when needed. Documenting risk triggers is part of the Plan Risk Responses process, which aims to develop options and actions to enhance opportunities and reduce threats to project objectives.Reference:The Standard for Risk Management in Portfolios, Programs, and Projects, page 78; PMBOK Guide, 6th edition, page 402.

In qualitative risk analysis, in addition to probability and impact, other factors can be used to refine the risk prioritization. Three valid factors to consider are:

1. Urgency: This refers to the timeframe within which a risk is likely to occur or the speed at which it might impact the project. High urgency risks require quicker responses, making them more critical in prioritization.

2. Proximity: This factor considers the time until the risk might affect the project. Risks that are likely to occur sooner may be given higher priority because they may require immediate attention.

3. Detectability: This assesses how easily the presence or impact of a risk can be identified. Risks that are hard to detect might be more dangerous and may require more resources to monitor and manage.

These factors are mentioned in PMI's guidelines for qualitative risk analysis as they provide a more nuanced view of risks beyond just probability and impact, allowing for more targeted and effective risk management strategies.

A risk trigger is a specific event or condition that signals that a risk is about to occur or has occurred. PMBOK Guide clarifies:

'Risk triggers (sometimes called warning signs) are indicators or symptoms that a risk event is about to occur. The risk register should include identified triggers for each risk.'

--- PMBOK Guide, 6th Edition, Section 11.2.3.1

Thus, documenting the specific event or condition (such as the supplier missing a delivery deadline) is the correct approach.

PMBOK Guide, 6th Edition, Section 11.2.3.1

Practice Standard for Project Risk Management, PMI, Section 5.3

Variance analysis is a method used to compare planned project performance against actual performance. Since the project sponsor has requested a performance report for the entire 10-year initiative, variance analysis would allow the risk manager to identify discrepancies between what was planned and what has been achieved over the course of the project. This analysis is crucial for understanding performance trends, cost deviations, schedule variations, and overall project health.

PMI's guidelines support the use of variance analysis in performance reporting as it provides insights into how well the project is adhering to its planned budget, schedule, and scope.