【文章內(nèi)容簡介】 – 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. 1130 Quantitative Risk Analysis ? Determine probability of achieving a specific project objective ? Quantify the risk exposure for the project, and determine the size of cost and schedule contingency reserves that may be needed ? Identify risks requiring the most attention by quantifying their relative contribution to project risk ? Identify achievable and realistic cost, schedule, or scope targets Measuring numerically the probability and consequences of risks and estimating their implication for project objectives 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. 1132 Inputs ? Risk Management Plan ? Identified Risks ? List of Prioritized Risks ? List of Risks for Additional Analysis and Management ? Historical Information – on prior, similar pleted projects, studies of similar projects by risk specialists, and risk databases available ? Expert Judgment – inputs from the project team, other subject matter experts within the anization, and outside sources ? Other Planning Outputs – schedule logic and duration estimates, WBS list of all cost elements, and models of project technical objectives 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. 1134 ? Probability – Likelihood of occurrence. (Number of occurrences of an event divided by the total number of all possible occurrences) ? Statistics – Mean – Average of the values of events – Mode – Value which occurs most often – Median – Value in middle of the range of ordered values ? Variance – Average of the squared deviations from the mean – Standard deviation – Square Root of the Variance – Range – Values between upper lower limits Tools Techniques (cont.) 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. 1136 Three values with probabilities。 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. 1137 Tools Techniques (cont.) Project A Project B 0.4 Success Failure Success Failure What is the probability that Project B will be selected and will be successful? Example Answer: 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 value 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. 1140 Tools Techniques ? Sensitivity Analysis – determines which risks have the most potential impact on the project ? Decision Tree Analysis – use of a diagram that describes a decision under consideration and the implications of choosing one or another of the available alternatives ? 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 when all the uncertain implications, costs, rewards, and subsequent decisions are quantified 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