11.4 PERFORM QUANTITATIVE RISK ANALYSIS Copyright 2017. Project Management Institute. All rights reserved. May not be reproduced in any form without permission from the publisher, except fair uses permitted under U.S. or applicable copyright law. Perform Quantitative Risk Analysis is the process of numerically analyzing the combined effect of identified individual project risks and other sources of uncertainty on overall project objectives. The key benefit of this process is that it quantifies overall project risk exposure, and it can also provide additional quantitative risk information to support risk response planning. This process is not required for every project, but where it is used, it is performed throughout the project. The inputs and outputs of this process are depicted in Figure 11-11. Figure 11-12 depicts the data flow diagram for the process. Perform Quantitative Risk Analysis Inputs .1 Project management plan • Risk management plan • Scope baseline • Schedule baseline • Cost baseline .2 Project documents • Assumption log • Basis of estimates • Cost estimates • Cost forecasts • Duration estimates • Milestone list • Resource requirements • Risk register • Risk report • Schedule forecasts .3 Enterprise environmental factors .4 Organizational process assets Tools & Techniques .1 Expert judgment .2 Data gathering • Interviews .3 Interpersonal and team skills • Facilitation .4 Representations of uncertainty .5 Data analysis • Simulation • Sensitivity analysis • Decision tree analysis • Influence diagrams Outputs .1 Project documents updates • Risk report Figure 11-11. Perform Quantitative Risk Analysis: Inputs, Tools & Techniques, and Outputs 428 Part 1 - Guide EBSCO Publishing : eBook Collection (EBSCOhost) - printed on 6/8/2021 6:59 PM via COLORADO STATE UNIVERSITY - GLOBAL CAMPUS AN: 1595321 ; Project Management Institute.; A Guide to the Project Management Body of Knowledge (PMBOK(R) GuideSixth Edition / Agile Practice Guide Bundle Account: ns125356.main.ehost Project Management Plan Project management plan • Risk management plan • Scope baseline • Schedule baseline • Cost baseline Project Documents Project documents • Assumption log • Basis of estimates • Cost estimates • Cost forecasts • Duration estimates • Milestone list • Resource requirements • Risk register • Risk report • Schedule forecasts 11.4 Perform Quantitative • Project Risk Analysis charter Project Documents Project documents updates • Risk report Enterprise/ Organization • Enterprise environmental factors • Organizational process assets Figure 11-12. Perform Quantitative Risk Analysis: Data Flow Diagram Perform Quantitative Risk Analysis is not required for all projects. Undertaking a robust analysis depends on the availability of high-quality data about individual project risks and other sources of uncertainty, as well as a sound underlying project baseline for scope, schedule, and cost. Quantitative risk analysis usually requires specialized risk software and expertise in the development and interpretation of risk models. It also consumes additional time and cost. The use of quantitative risk analysis for a project will be specified in the project’s risk management plan. It is most likely appropriate for large or complex projects, strategically important projects, projects for which it is a contractual requirement, or projects in which a key stakeholder requires it. Quantitative risk analysis is the only reliable method to assess overall project risk through evaluating the aggregated effect on project outcomes of all individual project risks and other sources of uncertainty. Perform Quantitative Risk Analysis uses information on individual project risks that have been assessed by the Perform Qualitative Risk Analysis process as having a significant potential to affect the project’s objectives. Outputs from Perform Quantitative Risk Analysis are used as inputs to the Plan Risk Responses process, particularly in recommending responses to the level of overall project risk and key individual risks. A quantitative risk analysis may also be undertaken following the Plan Risk Responses process, to determine the likely effectiveness of planned responses in reducing overall project risk exposure. 429 EBSCOhost - printed on 6/8/2021 6:59 PM via COLORADO STATE UNIVERSITY - GLOBAL CAMPUS. All use subject to https://www.ebsco.com/terms-of-use 11.4.1 PERFORM QUANTITATIVE RISK ANALYSIS: INPUTS 11.4.1.1 PROJECT MANAGEMENT PLAN Described in Section 4.2.3.1. Project management plan components include but are not limited to: uu Risk management plan. Described in Section 11.1.3.1. The risk management plan specifies whether quantitative risk analysis is required for the project. It also details the resources available for the analysis and the expected frequency of analyses. uu Scope baseline. Described in Section 5.4.3.1. The scope baseline describes the starting point from which the effect of individual project risks and other sources of uncertainty are evaluated. uu Schedule baseline. Described in Section 6.5.3.1. The schedule baseline describes the starting point from which the effect of individual project risks and other sources of uncertainty can be evaluated. uu Cost baseline. Described in Section 7.3.3.1. The cost baseline describes the starting point from which the effect of individual project risks and other sources of uncertainty can be evaluated. 11.4.1.2 PROJECT DOCUMENTS Project documents that can be considered as inputs for this process include but are not limited to: uu Assumption log. Described in Section 4.1.3.2. Assumptions may form inputs to the quantitative risk analysis if they are assessed as posing a risk to project objectives. The effect of constraints may also be modeled during a quantitative risk analysis. uu Basis of estimates. Described in Sections 6.4.3.2 and 7.2.3.2. The basis of estimates used in the planning of the project may be reflected in variability modeled during a quantitative risk analysis process. This may include information on the estimate’s purpose, classification, assumed accuracy, methodology, and source. uu Cost estimates. Described in Section 7.2.3.1. Cost estimates provide the starting point from which cost variability is evaluated. uu Cost forecasts. Described in Section 7.4.3.2. Forecasts such as the project’s estimate to complete (ETC), estimate at completion (EAC), budget at completion (BAC), and to-complete performance index (TCPI) may be compared to the results of a quantitative cost risk analysis to determine the confidence level associated with achieving these targets. uu Duration estimates. Described in Section 6.4.3.1. Duration estimates provide the starting point from which schedule variability is evaluated. uu Milestone list. Described in Section 6.2.3.3. Significant events in the project define the schedule targets against which the results of a quantitative schedule risk analysis are compared, in order to determine the confidence level associated with achieving these targets. 430 Part 1 - Guide EBSCOhost - printed on 6/8/2021 6:59 PM via COLORADO STATE UNIVERSITY - GLOBAL CAMPUS. All use subject to https://www.ebsco.com/terms-of-use uu Resource requirements. Described in Section 9.2.3.1. Resource requirements provide the starting point from which variability is evaluated. uu Risk register. Described in Section 11.2.3.1. The risk register contains details of individual project risks to be used as input for quantitative risk analysis. uu Risk report. Described in Section 11.2.3.2. The risk report describes sources of overall project risk and the current overall project risk status. uu Schedule forecasts. Described in Section 6.6.3.2. Forecasts may be compared to the results of a quantitative schedule risk analysis to determine the confidence level associated with achieving these targets. 11.4.1.3 ENTERPRISE ENVIRONMENTAL FACTORS The enterprise environmental factors that can influence the Perform Quantitative Risk Analysis process include but are not limited to: uu Industry studies of similar projects, and uu Published material, including commercial risk databases or checklists. 11.4.1.4 ORGANIZATIONAL PROCESS ASSETS The organizational process assets that can influence the Perform Quantitative Risk Analysis process include information from similar completed projects. 11.4.2 PERFORM QUANTITATIVE RISK ANALYSIS: TOOLS AND TECHNIQUES 11.4.2.1 EXPERT JUDGMENT Described in Section 4.1.2.1. Expertise should be considered from individuals or groups with specialized knowledge or training in the following topics: uu Translating information on individual project risks and other sources of uncertainty into numeric inputs for the quantitative risk analysis model, uu Selecting the most appropriate representation of uncertainty to model particular risks or other sources of uncertainty, uu Modeling techniques that are appropriate in the context of the project, uu Identifying which tools would be most suitable for the selected modeling techniques, and uu Interpreting the outputs of quantitative risk analysis. 431 EBSCOhost - printed on 6/8/2021 6:59 PM via COLORADO STATE UNIVERSITY - GLOBAL CAMPUS. All use subject to https://www.ebsco.com/terms-of-use 11.4.2.2 DATA GATHERING Interviews (see Section 5.2.2.2) may be used to generate inputs for the quantitative risk analysis, drawing on inputs that include individual project risks and other sources of uncertainty. This is particularly useful where information is required from experts. The interviewer should promote an environment of trust and confidentiality during the interview to encourage honest and unbiased contributions. 11.4.2.3 INTERPERSONAL AND TEAM SKILLS Interpersonal and team skills that can be used for this process include but are not limited to facilitation (see Section 4.1.2.3). A skilled facilitator is useful for gathering input data during a dedicated risk workshop involving project team members and other stakeholders. Facilitated workshops can improve effectiveness by establishing a clear understanding of the purpose of the workshop, building consensus among participants, ensuring continued focus on the task, and using creative approaches to deal with interpersonal conflict or sources of bias. 11.4.2.4 REPRESENTATIONS OF UNCERTAINTY Quantitative risk analysis requires inputs to a quantitative risk analysis model that reflect individual project risks and other sources of uncertainty. Where the duration, cost, or resource requirement for a planned activity is uncertain, the range of possible values can be represented in the model as a probability distribution. This may take several forms. The most commonly used are triangular, normal, lognormal, beta, uniform, or discrete distributions. Care should be taken when selecting an appropriate probability distribution to reflect the range of possible values for the planned activity. Individual project risks may be covered by probability distributions. Alternatively, risks may be included in the model as probabilistic branches, where optional activities are added to the model to represent the time and/or cost impact of the risk should it occur, and the chance that these activities actually occur in a particular simulation run matches the risk’s probability. Branches are most useful for risks that might occur independently of any planned activity. Where risks are related, for example, with a common cause or a logical dependency, correlation is used in the model to indicate this relationship. Other sources of uncertainty may also be represented using branches to describe alternative paths through the project. 432 Part 1 - Guide EBSCOhost - printed on 6/8/2021 6:59 PM via COLORADO STATE UNIVERSITY - GLOBAL CAMPUS. All use subject to https://www.ebsco.com/terms-of-use 11.4.2.5 DATA ANALYSIS Data analysis techniques that can be used during this process include but are not limited to: uu Simulation. Quantitative risk analysis uses a model that simulates the combined effects of individual project risks and other sources of uncertainty to evaluate their potential impact on achieving project objectives. Simulations are typically performed using a Monte Carlo analysis. When running a Monte Carlo analysis for cost risk, the simulation uses the project cost estimates. When running a Monte Carlo analysis for schedule risk, the schedule network diagram and duration estimates are used. An integrated quantitative cost-schedule risk analysis uses both inputs. The output is a quantitative risk analysis model. Computer software is used to iterate the quantitative risk analysis model several thousand times. The input values (e.g., cost estimates, duration estimates, or occurrence of probabilistic branches) are chosen at random for each iteration. Outputs represent the range of possible outcomes for the project (e.g., project end date, project cost at completion). Typical outputs include a histogram presenting the number of iterations where a particular outcome resulted from the simulation, or a cumulative probability distribution (S-curve) representing the probability of achieving any particular outcome or less. An example S-curve from a Monte Carlo cost risk analysis is shown in Figure 11-13. Range of Uncertainty 100 100 90 90 85% Chance of Costing $2.45M or Less Expected Value $2.35M 70 60 30 70 60 Target $2.2M 50 40 80 50 40 23% Chance of Meeting Target 30 20 20 10 10 0 0 $2.0M $2.1M $2.2M $2.3M $2.4M $2.5M $2.6M $2.7M Cumulative Probability (%) Cumulative Probability (%) 80 $2.8M Predicted Total Project Cost Figure 11-13. Example S-Curve from Quantitative Cost Risk Analysis 433 EBSCOhost - printed on 6/8/2021 6:59 PM via COLORADO STATE UNIVERSITY - GLOBAL CAMPUS. All use subject to https://www.ebsco.com/terms-of-use For a quantitative schedule risk analysis, it is also possible to conduct a criticality analysis that determines which elements of the risk model have the greatest effect on the project critical path. A criticality index is calculated for each element in the risk model, which gives the frequency with which that element appears on the critical path during the simulation, usually expressed as a percentage. The output from a criticality analysis allows the project team to focus risk response planning efforts on those activities with the highest potential effect on the overall schedule performance of the project. uu Sensitivity analysis. Sensitivity analysis helps to determine which individual project risks or other sources of uncertainty have the most potential impact on project outcomes. It correlates variations in project outcomes with variations in elements of the quantitative risk analysis model. One typical display of sensitivity analysis is the tornado diagram, which presents the calculated correlation coefficient for each element of the quantitative risk analysis model that can influence the project outcome. This can include individual project risks, project activities with high degrees of variability, or specific sources of ambiguity. Items are ordered by descending strength of correlation, giving the typical tornado appearance. An example tornado diagram is shown in Figure 11-14. Activity or Risk Driving Project Duration Activity B12.3 Manufacture reactors Risk 5.2 DCS may fail installation test Risk 5.7 Duplicate test may not be required Activity A3.12 Construct control room Risk 4.6 Piling contractor may deliver early Activity A7.1 Provide temporary facilities Activity D1.9 Install Equipment Risk 7.2 Hydrotest may find fewer faults -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 Correlation with Project Duration Figure 11-14. Example Tornado Diagram 434 Part 1 - Guide EBSCOhost - printed on 6/8/2021 6:59 PM via COLORADO STATE UNIVERSITY - GLOBAL CAMPUS. All use subject to https://www.ebsco.com/terms-of-use uu Decision tree analysis. Decision trees are used to support selection of the best of several alternative courses of action. Alternative paths through the project are shown in the decision tree using branches representing different decisions or events, each of which can have associated costs and related individual project risks (including both threats and opportunities). The end-points of branches in the decision tree represent the outcome from following that particular path, which can be negative or positive. The decision tree is evaluated by calculating the expected monetary value of each branch, allowing the optimal path to be selected. An example decision tree is shown in Figure 11-15. Decision Definition Decision to be Made Decision Node Input: Cost of Each Decision Output: Decision Made Chance Node Input: Scenario Probability, Reward if it Occurs Output: Expected Monetary Value (EMV) 60% Strong Demand ($200M) Build New Plant (Invest $120M) $36M = .60 ($80M) + .40 (–$30M) Build or Upgrade? Weak Demand ($90M) EMV of Build New Plant considering demand Decision EMV = $46M (the larger of $36M and $46M) Decision Node 40% 60% Strong Demand ($120M) Upgrade Plant (Invest $50M) Chance Node $46M = .60 ($70M) + .40 ($10M) End of Branch EMV of Upgrade Plant considering demand 40% Weak Demand ($60M) Net Path Value Computed: Payoffs minus Costs along Path $80M $80M = $200M – $120M -$30M –$30M = $90M – $120M $70M $70M = $120M – $50M $10M $10M = $60M – $50M Note 1: The decision tree shows how to make a decision between alternative capital strategies (represented as “decision nodes”) when the environment contains uncertain elements (represented as “chance nodes”). Note 2: Here, a decision is being made whether to invest $120M US to build a new plant or to instead invest only $50M US to upgrade the existing plant. For each decision, the demand (which is uncertain, and therefore represents a “chance node”) must be accounted for. For example, strong demand leads to $200M revenue with the new plant but only $120M US for the upgraded plant, perhaps due to capacity limitations of the upgraded plant. The end of each branch shows the net effect of the payoffs minus costs. For each decision branch, all effects are added (see shaded areas) to determine the overall Expected Monetary Value (EMV) of the decision. Remember to account for the investment costs. From the calculations in the shaded areas, the upgraded plant has a higher EMV of $46M – also the EMV of the overall decision. (This choice also represents the lowest risk, avoiding the worst case possible outcome of a loss of $30M). Figure 11-15. Example Decision Tree 435 EBSCOhost - printed on 6/8/2021 6:59 PM via COLORADO STATE UNIVERSITY - GLOBAL CAMPUS. All use subject to https://www.ebsco.com/terms-of-use uu Influence diagrams. Influence diagrams are graphical aids to decision making under uncertainty. An influence diagram represents a project or situation within the project as a set of entities, outcomes, and influences, together with the relationships and effects between them. Where an element in the influence diagram is uncertain as a result of the existence of individual project risks or other sources of uncertainty, this can be represented in the influence diagram using ranges or probability distributions. The influence diagram is then evaluated using a simulation technique, such as Monte Carlo analysis, to indicate which elements have the greatest influence on key outcomes. Outputs from an influence diagram are similar to other quantitative risk analysis methods, including S-curves and tornado diagrams. 11.4.3 PERFORM QUANTITATIVE RISK ANALYSIS: OUTPUTS 11.4.3.1 PROJECT DOCUMENTS UPDATES Project documents that can be considered as outputs for this process include but are not limited to the risk report described in Section 11.2.3.2. The risk report will be updated to reflect the results of the quantitative risk analysis. This will typically include: uu Assessment of overall project risk exposure. Overall project risk is reflected in two key measures: nnChances of project success, indicated by the probability that the project will achieve its key objectives (e.g., required end date or interim milestones, required cost target, etc.) given the identified individual project risks and other sources of uncertainty; and nnDegree of inherent variability remaining within the project at the time the analysis was conducted, indicated by the range of possible project outcomes. uu Detailed probabilistic analysis of the project. Key outputs from the quantitative risk analysis are presented, such as S-curves, tornado diagrams, and criticality analysis, together with a narrative interpretation of the results. Possible detailed results of a quantitative risk analysis may include: nnAmount of contingency reserve needed to provide a specified level of confidence; nnIdentification of individual project risks or other sources of uncertainty that have the greatest effect on the project critical path; and nnMajor drivers of overall project risk, with the greatest influence on uncertainty in project outcomes. uu Prioritized list of individual project risks. This list includes those individual project risks that pose the greatest threat or present the greatest opportunity to the project, as indicated by sensitivity analysis. uu Trends in quantitative risk analysis results. As the analysis is repeated at different times during the project life cycle, trends may become apparent that inform the planning of risk responses. uu Recommended risk responses. The risk report may present suggested responses to the level of overall project risk exposure or key individual project risks, based on the results of the quantitative risk analysis. These recommendations will form inputs to the Plan Risk Responses process. 436 Part 1 - Guide EBSCOhost - printed on 6/8/2021 6:59 PM via COLORADO STATE UNIVERSITY - GLOBAL CAMPUS. All use subject to https://www.ebsco.com/terms-of-use 
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