【正文】 s of its start. Project pletion dates toward the left have higher risk while those toward the right have lower risk. Quantitative Risk Analysis Source: PMBOK Guide 2023 Version 169。 2023 RobbinsGioia, Inc. 1141 Tools Techniques (cont.) Decide not to pursue $ 0 Production Successful Probability = High Demand Probability = $ 550,000 Decision Trees Production Unsuccessful Probability = Terminate = $ 200,000 Decide to pursue Low Demand Probability = $100,000 Expect Value of Pursuing Project A x x $ 550,000 = $ 115,500 x x – $ 100,000 = – $ 49,000 x – $ 200,000 = – $ 60,000 $ 6,500 The expected value of Project A is $6,500. The expected value of not preceding is $0. Preceding is the lucrative option. Quantitative Risk Analysis Source: PMBOK Guide 2023 Version 169。 2023 RobbinsGioia, Inc. 1139 Tools Techniques (cont.) Beta Distribution Triangular Distribution Mean = (a+m+b) / 3 Variance = [(ba)2 + (ma)(mb)] / 18 Using PERT approximations Mean = (a +4m +b) / 6 Variance = [(ba) / 6]2 Quantitative Risk Analysis Source: PMBOK Guide 2023 Version 169。 2023 RobbinsGioia, Inc. 1138 Tools Techniques (cont.) ? Probability distribution (Method of moments) – Calculates project range estimates ? Expected moary value – Probability times cost ? Three values – low (a) , most likely (m), and high (b) – with probabilities for each。 used to calculate expected values – Optimistic – Most likely – Pessimistic Tools Techniques (cont.) . Optimistic x $ 100 K = $ 20 K Most Likely x $ 130 K = $ 78 K Pessimistic x $ 180 K = $ 36 K Expected Value = $ 134 K Quantitative Risk Analysis Source: PMBOK Guide 2023 Version 169。 2023 RobbinsGioia, Inc. 1135 ? 2 standard deviations (+/ 1) = % ? 4 standard deviations (+/ 2) = % ? 6 standard deviations (+/ 3) = % 0 1 2 3 +1 +2 +3 Normal Distribution Curve Quantitative Risk Analysis Source: PMBOK Guide 2023 Version 169。 2023 RobbinsGioia, Inc. 1133 Tools Techniques ? Interviewing – project stakeholders and subjectmatter experts to quantify the probability and consequences of risks on project objectives ? The information needed depends upon the type of probability distributions that will be used Quantitative Risk Analysis Source: PMBOK Guide 2023 Version 169。 2023 RobbinsGioia, Inc. 1131 Quantitative Risk Analysis Outputs ? Prioritized List of Quantified Risks ? Probability Analysis of the project ? Probability of achieving the cost and time objectives ? Trends in Quantitative Risk Analysis Results Inputs ? Risk Management Plan ? List of prioritized risks ? List of risks for additional Management Analysis ? Historical Information ? Expert Judgment ? Other Planning Outputs Tools Techniques ? Interviewing ? Sensitivity Analysis ? Decision Tree Analysis ? Simulation Source: PMBOK Guide 2023 Version 169。 2023 RobbinsGioia, Inc. 1129 Outputs (cont.) ? List of Risks for Additional Analysis and Management – moderate and high risks are candidates for more analysis, including quantitative and risk analysis, and risk management action ? Trends in Qualitative Risk Analysis Results – As the analysis is repeated, a trend of results may bee apparent, and can make risk response more or less urgent and important Qualitative Risk Analysis Source: PMBOK Guide 2023 Version 169。 2023 RobbinsGioia, Inc. 1127 Tools Techniques ? Project Assumption Testing – Assumptions are tested against two criteria: assumption stability and the consequences on the project if the assumption is false ? Data Precision Ranking – is a technique to evaluate the degree to which the data is useful ? Extent of understanding of the risk ? Data available about the risk ? Quality of the data ? Reliability and integrity of the data Qualitative Risk Analysis Source: PMBOK Guide 2023 Version 169。 2023 RobbinsGioia, Inc. 1125 Inputs (cont.) ? Data Precision – measures the extent of data available, as well as the reliability of the data and source of the data ? Scales of Probability and Impact – assess the two key dimensions of risk (probability of occurring and impact on project) ? Assumptions Qualitative Risk Analysis Source: PMBOK Guide 2023 Version 169。 2023 RobbinsGioia, Inc. 1123 Qualitative Risk Analysis Outputs ? Overall risk ranking ? List of prioritized tasks ? List of risks for additional Management Analysis ? Trends in results Inputs ? Risk Management Plan ? Identified risks ? Project status ? Project type ? Data Precision ? Scales of probability impact ? Assumptions Tools Techniques ? Risk probability impact ? Risk rating matrix ? Project assumptions testing ? Data precision ranking Source: PMBOK Guide 2023 Version 169。 2023 RobbinsGioia, Inc. 1121 Outputs ? Potential Risk Event – Identify discrete occurrences that might affect the project ? Triggers – Risk symptoms or warning signs that indicate a risk even has occurred or is about to occur ? Inputs to other processes – may identify a need for further activity in another area ? Risks are often input to other processes as constraints or assumptions Risk Identification Source: PMBOK Guide 2023 Version 169。 2023 RobbinsGioia, Inc. 1119 Tools Techniques ? Assumptions Analysis – technique that examines the validity of assumptions to identify risks to project because of invalid assumptions ? Diagramming techniques – ? Cause and effect diagrams used to identify causes of risks ? System or process flow charts that show how various elements of a system interrelate and the causes of risks ? Influence diagrams the graphically represent a problem showing causal influences, time ordering events and other relat