A decision tree analysis is a tool that helps to evaluate and select the best option among different alternatives based on costs and probabilities. A decision tree analysis uses a graphical representation of a decision problem, where each node represents a decision point, a chance event, or an outcome. The branches of the tree show the possible choices, events, or consequences that can occur at each node. The end nodes of the tree show the expected value or payoff of each option, which is calculated by multiplying the probability and the cost or benefit of each outcome. A decision tree analysis can help to compare the expected values of different options and choose the one that maximizes the benefit or minimizes the cost1. A decision tree analysis can also help to incorporate uncertainty and risk into the decision making process, as it shows the range of possible outcomes and their likelihoods2. Therefore, the project manager should perform a decision tree analysis to evaluate and select the best option based on costs and probabilities for a mega facility development project. Performing a FMECA fault tree analysis, conducting a sensitivity analysis, or conducting an analytic hierarchy process are not the best options to evaluate and select the best option based on costs and probabilities. A FMECA fault tree analysis is a tool that helps to identify and analyze the potential causes and effects of failures in a system or process. It uses a graphical representation of a failure event, where each node represents a basic or intermediate event that contributes to the failure. The branches of the tree show the logical relationships between the events, using AND or OR gates. A FMECA fault tree analysis can help to calculate the probability and severity of failures, as well as to prioritize and mitigate the risks3. However, a FMECA fault tree analysis does not help to compare different options or alternatives, as it focuses on a single failure scenario. Conducting a sensitivity analysis is a tool that helps to measure how the uncertainty in the input variables of a model affects the output or outcome of the model. It uses a graphical or numerical representation of the relationship between the input and output variables, showing how the output changes when the input changes. A sensitivity analysis can help to identify the most critical or influential variables, as well as to test the robustness or reliability of the model4. However, a sensitivity analysis does not help to compare different options or alternatives, as it focuses on a single model or option. Conducting an analytic hierarchy process is a tool that helps to evaluate and select the best option among different alternatives based on multiple criteria. It uses a mathematical method of pairwise comparison, where each alternative is compared to each other in terms of each criterion. The results of the comparisons are then aggregated into a matrix, which shows the relative importance or preference of each alternative. An analytic hierarchy process can help to rank the alternatives and choose the one that best satisfies the criteria5. However, an analytic hierarchy process does not help to incorporate costs and probabilities into the decision making process, as it relies on subjective judgments and preferences. References: 1, 2, 3, 4, 5.
A decision tree analysis is a quantitative risk analysis technique that helps evaluate and select the best option based on costs and probabilities. It visually represents different decision paths and their associated probabilities, allowing the project manager to compare and select the most appropriate option for the project.

The project manager should escalate this initiative to project decision makers and sponsors, as they have the authority to approve changes in budget and scope. They can evaluate the potential benefits and associated with the new technology and make an informed decision on whether to proceed.
According to the PMBOKGuide1, an opportunity is a risk that would have a positive effect on one or more project objectives if it occurs. Opportunities are uncertain events or conditions that can enhance or facilitate the achievement of project goals, such as cost savings, schedule acceleration, quality improvement, or scope expansion. A project manager should take advantage of opportunities by implementing risk responses that seek to maximize their probability and/or positive impact. In this case, the project manager wants to introduce a new technology to improve the project's performance, which is an opportunity for the project. The project manager should take advantage of this opportunity by planning and executing appropriate risk responses, such as exploiting, enhancing, sharing, or accepting the opportunity. This is part of the Plan Risk Responses and Implement Risk Responses processes in the PMBOKGuide1. References: 1: A Guide to the Project Management Body of Knowledge (PMBOKGuide) - Sixth Edition.

The stakeholders should prepare a risk-adjusted backlog when making decisions on how to respond to known and new risks. A risk-adjusted backlog helps prioritize work items based on their risk level and potential impact on the project.
A risk-adjusted backlog is an artifact that reflects the prioritization of the product backlog items based on their risk exposure. It is used to plan for the execution phase of an agile project, where the stakeholders can decide how to respond to known and new risks by selecting the most valuable and least risky items to deliver.
A risk-adjusted backlog can help the stakeholders to optimize the value delivery and reduce the uncertainty of the project outcomes. References: PMI, The Standard for Risk Management in Portfolios, Programs, and Projects, 2019, p. 113; PMI, Agile Practice Guide, 2017, p. 54.

Residual risks are the risks that remain after the risk response plan has been implemented. They are the risks that are accepted by the project team and stakeholders as part of the project. Residual risks may have low probability or impact, but they still need to be monitored and controlled throughout the project. The first thing that the risk manager should do when a risk owner identifies and reports some residual risks is to analyze, document, and communicate them to the relevant stakeholders. The risk manager should assess the probability and impact of the residual risks, and determine if they require any further response or contingency plan. The risk manager should also update the risk register and the risk report with the information about the residual risks, and share them with the stakeholders who need to be aware of them. This will help the project team and stakeholders to be prepared for any potential occurrence of the residual risks, and to take appropriate actions if needed. References: PMI, The Standard for Risk Management in Portfolios, Programs, and Projects, 2019, p.
94-95, 101.

The risk manager should perform a quantitative risk analysis to determine the potential impact of risks on the project's completion date. This will help in providing a more accurate project completion date to the customer, considering the risks and their potential effects on the project schedule.
According to the PMI Risk Management Professional (PMI-RMP)®Examination Content Outline1, one of the tasks in the domain of Risk Analysis is to perform quantitative risk analysis using techniques such as Monte Carlo simul-ation, decision tree analysis, sensitivity analysis, etc., to quantify the possible outcomes for the project and their probabilities, and to evaluate the cost and schedule impacts of risks1. In this scenario, the risk manager should perform a quantitative risk analysis and update the results, because the project costs have increased significantly and the customer has imposed a strict deadline for the project completion. A quantitative risk analysis will help the risk manager to estimate the probability of meeting the project objectives, such as cost and schedule, and to determine the appropriate contingency reserves for the project. A quantitative risk analysis will also provide more accurate and reliable information for the customer and the project team, and will support the risk response planning process2. References: 1: PMI Risk Management Professional (PMI-RMP)®Examination Content Outline, page 92: A Guide to the Project Management Body of Knowledge (PMBOKGuide) - Sixth Edition, pages 431-432.