11.4.1 Inputs to Quantitative Risk Analysis

.1 Risk management plan. This plan is described in Section 11.1.3.

.2 Identified risks. These are described in Section 11.2.3.1.

.3 List of prioritized risks. This is described in Section 11.3.3.2.

.4 List of risks for additional analysis and management. This is described in Section 11.3.3.3.

.5 Historical information. Information on prior, similar completed projects, studies of similar projects by risk specialists, and risk databases that may be available from industry or proprietary sources (see Section 11.2.1.4).

.6 Expert judgment. Input may come from the project team, other subject matter experts in the organization, and from others outside the organization. Other sources of information include engineering or statistical experts (see Section 5.1.2.2).

.7 Other planning outputs. Most helpful planning outputs are the project logic and duration estimates used in determining schedules, the WBS listing of all cost elements with cost estimates, and models of project techinical objectives.

11.4.2 Tools and Techniques for Quantitative Risk Analysis

.1 Interviewing. Interviewing techniques are used to quantify the probability and consequences of risks on project objetives. A risk interview with project stakeholders and subject-matter expert may be the first step in quantifying risks. The information needed depends upon the type of probability distributions that will be used. For instance, information would be gathered on the optimistic (low), pessimistic (high), and the most likely scenarios if triangular distributions are used, or on mean and standard deviation for the normal and log normal distributions. Examples of three-point estimates for a cost estimate are shown in Figure 11-4.
  Continuos probability distributions are usually used in quantitative risk analysis. Distributions represent both probability and consequences of the project component. Common distribution types include the uniform, normal, triangular, beta, and log normal. Two examples of these distributions are shown in Figure 11-5 (where the vertical axis refers to probability and the horizontal axis to impact).
  Documenting the rationale of the risk rangers is an important component of the risk interview, because it can lead to effective strategies for risk response in the risk response planning process, described in Section 11.5).

.2 Sensitivity analysis.. Sensitivity analysis helps to determine which risks have the most potenttial impact on the project. It examines the extent to which the uncertainty of each project element affects the objective being examined when all other uncertain elements are held at their baseline values.

.3 Decision tree analysis. A decision analysis is usually structured as a decision tree. The decision tree is a diagram that describes a decision under consideration and the implications of choosing one or another of the available alternatives. It incorporates probabilities of risks and the costs or rewards of each logical path of events and future decisions. Solving the decision tree indicates which decision yields the greatest expected value to the decision-maker when all the uncertain implications, costs, rewards, and subsequent decisions are quantified. A decision tree is shown in Figure 11-6.

.4 Simulation.. A project simulation uses a model that translates the uncertainties specified at a detailed level into their potential impact on objectives that are expressed at the level of the total project. Project simulations are typically performed using the Monte Carlo technique.
  For a cost risk analysis, a simulation may use the traditional project WBS as its model. For a schedule risk analysis, the Precedence Diagramming Method (PDM) schedule is used (see Section 6.2.2.1).
  A cost risk simulation results is shown in Figure 11-7

11.4.3 Outputs from Quantitative Risk Analysis

.1 Prioritized list of quantified risks. This list of risks includes those that pose the greatest threat or present the greatest opportunity to the project together with a measure of their impact.

.2 Probabilistic analysis of the project. Forecasts of potential project schedule and cost results listing the possible completion dates or project duration and costs with their associated confidence levels.

.3 Probability of achieving the cost and time objectives. The probability of achieving the project objectives under the current plan and with the current knowledgeof the risks facing the project can be estimated using quantitative risk.

.4 Trends in quantitative risk analysis results. As the analysis is repeated, a trend of results may become apparent.