Adding quantitative risk analysis your Swiss Army Knife

Project Context Projects are the result of business investment decisions Investors seek returns commensurate with risk and resources committed Public sector, private sector, non- profits Monetary or mission-success returns ©Square Peg Consulting, 2010, all rights reserved

Balancing the Project Investor Project Manager Business driven Charter specified outcomes outcomes Deterministic, limited, Resources estimates resources with variation Risk proportional to Risk driven by internal expected reward & external events and Unknowing of conditions implementation Details drive risk details assessments and resource estimates ©Square Peg Consulting, 2010, all rights reserved

Risk balances Value with Capacity Project Value from Project Estimate from the Top Down the Bottom Up Risk Investor’s Resource Commitment Scope Time Resources Management’s Expected Project’s Employment Return on Investment of Investment ©Square Peg Consulting, 2010, all rights reserved

Managing risk All plans have uncertainties, and thus outcomes are at risk Probabilities and statistics are important data to understand and deal with uncertainties Information provides insight for problem avoidance ©Square Peg Consulting, 2010, all rights reserved

Why apply risk analysis to schedules? Determine the likelihood of overrunning the schedule Find architectural weakness in the schedule Estimate risk needed to balance investor commitment ©Square Peg Consulting, 2010, all rights reserved

Quantitative Methods Statistics and Probabilities are the main tools Important equations and most useful distributions are found in the PMBOK Triangular & Beta distributions simulate many project situations Asymmetry is key to “real world” estimates ©Square Peg Consulting, 2010, all rights reserved

The Math of Distributions Averages of independent distributions can be added Variances of independent distributions can be added Most Likely’s can not be added CPM dates are deterministic, but if taken from distributions, they should not be “most likely’s” ©Square Peg Consulting, 2010, all rights reserved

Managing “Long Task Duration” Risk Path 1.0: 60 work days Baseline 1/1 Long task 3/25 Replanned CPM Date 1.1 short task 1/1 1.2 3/15 1.3 1/21 3/25 2/12 1.4 ©Square Peg Consulting, 2010, all rights reserved

Variance improved by 1/N Managing D uration Risk Work Breakdow n Triangle Probability Distribution of Duration Structure of Variance Standard Scheduled Minimum Most Maximum (Days- Deviation Activities in Days [-10% ] Likely [+30% ] Average squared) (D ays) WBS Activity 1.0 (Baseline) 54 60 78 64.00 26.00 5.10 Baseline restructured into four subtasks and a summ ary task WBS Activity 1.1 13.5 15 19.5 16.00 1.63 1.27 WBS Activity 1.2 13.5 15 19.5 16.00 1.63 1.27 WBS Activity 1.3 18 20 26 21.33 2.89 1.70 WBS Activity 1.4 9 10 13 10.67 0.72 0.85 WBS Activity 1.0 Summary (New Distribution Unknown B aseline) 64.00 6.86 2.62 Average = [min + m ax + most likely]/3 No 74% 49% Variance = [[max-m in][max-min] + change improved improved [most likely - min][most likely - max]]/18 from from from Standard Deviation = sq root [Variance] Baseline Baseline Baseline ©Square Peg Consulting, 2010, all rights reserved

Applying the Math Average may not improve with task subdivision Sum of the Averages, 64 days, is the average of the Summary task Variance is reduced by subdividing tasks into independent sub-tasks Variances of independent tasks add ©Square Peg Consulting, 2010, all rights reserved

Monte Carlo Simulation Automates the tedium of calculations “Runs” the project schedule many times, independently Each “run” uses the probability distribution to determine a duration for each task, run- by-run Result is a distribution of outcomes ©Square Peg Consulting, 2010, all rights reserved

1/1 60 work days 1.1 1.2 3/15 1.3 1/21 1.4 3/25 2/12 Date: 3/9/99 10:30:27 PM Completion Std Deviation: 2.4d σ results Number of Samples: 1000 Unique ID: 6 95% Confidence Interval: 0.1d Each bar represents 1d. Calculated 2.62, Name: Task 1.4 170 1.0 Simulation 2.4 Completion Probability Table 153 0.9 Prob Date Prob Date Cumulative Probability 136 0.8 0.05 3/25/99 0.55 3/31/99 119 0.7 0.10 3/25/99 0.60 3/31/99 0.15 3/26/99 0.65 4/1/99 102 0.6 Sample Count 0.20 3/26/99 0.70 4/1/99 85 0.5 0.25 3/29/99 0.75 4/1/99 68 0.4 0.30 3/29/99 0.80 4/2/99 0.35 3/29/99 0.85 4/2/99 51 0.3 0.40 3/30/99 0.90 4/5/99 34 0.2 0.45 3/30/99 0.95 4/6/99 17 0.1 0.50 3/30/99 1.00 4/9/99 3/23/99 3/31/99 4/9/99 Completion Date Monte Carlo Simulation proves the calculations ©Square Peg Consulting, 2010, all rights reserved

1/1 60 work days 1.1 1.2 3/15 1.3 1/21 1.4 3/25 2/12 Date: 3/9/99 10:30:27 PM Completion Std Deviation: 2.4d Cumulative Number of Samples: 1000 Probability of 3/25 = 95% Confidence Interval: 0.1d Unique ID: 6 Each bar represents 1d. Probability Name: Task 1.4 0.1 or less 170 1.0 Completion Probability Table 153 0.9 Prob Date Prob Date Cumulative Probability 136 0.8 0.05 3/25/99 0.55 3/31/99 119 0.7 0.10 3/25/99 0.60 3/31/99 0.15 3/26/99 0.65 4/1/99 102 0.6 Sample Count 0.20 3/26/99 0.70 4/1/99 85 0.5 0.25 3/29/99 0.75 4/1/99 68 0.4 0.30 3/29/99 0.80 4/2/99 0.35 3/29/99 0.85 4/2/99 51 0.3 0.40 3/30/99 0.90 4/5/99 34 0.2 0.45 3/30/99 0.95 4/6/99 17 0.1 0.50 3/30/99 1.00 4/9/99 3/23/99 3/31/99 4/9/99 Completion Date 3/25 is 5% probable ©Square Peg Consulting, 2010, all rights reserved

More Schedule Math “Joint Probabilities” describes the probability of occurrence two or more independent events Joint Probability is the product of the individual probabilities Important tool for schedule analysis of joining or merging tasks ©Square Peg Consulting, 2010, all rights reserved

Joining tasks have Merge Bias Cumulative Probability P1 Task 1 Task 2 Task 1 & 2 P2 P3=P1*P2 D1 D2 Date Task 1 & 2 at Task 1& 2 at Date D2 Date D1 with with cum probability cum P2 probability P3 ©Square Peg Consulting, 2010, all rights reserved

1/1 60 work days 1.1 1.2 3/15 1.3 1/21 1.4 3/25 2/12 Date: 3/9/99 10:30:27 PM Completion Std Deviation: 2.4d Number of Samples: 1000 Probability of 3/30 = 95% Confidence Interval: 0.1d Unique ID: 6 Each bar represents 1d. Name: Task 1.4 0.5 or less 170 1.0 Completion Probability Table 153 0.9 Prob Date Prob Date Cumulative Probability 136 0.8 0.05 3/25/99 0.55 3/31/99 119 0.7 0.10 3/25/99 0.60 3/31/99 0.15 3/26/99 0.65 4/1/99 102 0.6 Sample Count 0.20 3/26/99 0.70 4/1/99 85 0.5 0.25 3/29/99 0.75 4/1/99 68 0.4 0.30 3/29/99 0.80 4/2/99 0.35 3/29/99 0.85 4/2/99 51 0.3 0.40 3/30/99 0.90 4/5/99 34 0.2 0.45 3/30/99 0.95 4/6/99 17 0.1 0.50 3/30/99 1.00 4/9/99 3/23/99 3/31/99 4/9/99 Completion Date 3/30 is the 50% probable date for the milestone ©Square Peg Consulting, 2010, all rights reserved

1/21 3/15 1/1 2/12 3/25 Project 2: 60 work days 3/15 1/21 2 parallel 4-task paths 2/12 3/25 Date: 3/8/99 9:31:06 PM Completion Std Deviation: 2.0d Number of Samples: 2000 ProbabilityInterval: 0.1d = 0.5 * 0.5 = 0.25 or 95% Confidence of 3/30 Unique ID: 12 Each bar represents 1d. Name: Finish Milestone less 380 1.0 Completion Probability Table 342 0.9 Prob Date Prob Date 304 0.8 0.05 3/29/99 0.55 4/1/99 Cumulative Probability 266 0.7 0.10 3/29/99 0.60 4/1/99 Sample Count 0.15 3/30/99 0.65 4/2/99 228 0.6 0.20 3/30/99 0.70 4/2/99 190 0.5 0.25 3/30/99 0.75 4/2/99 152 0.4 0.30 3/31/99 0.80 4/2/99 0.35 3/31/99 0.85 4/5/99 114 0.3 0.40 3/31/99 0.90 4/5/99 76 0.2 0.45 3/31/99 0.95 4/6/99 38 0.1 0.50 4/1/99 1.00 4/12/99 3/24/99 4/1/99 4/12/99 Completion Date Parallel Paths cause “shift right” bias ©Square Peg Consulting, 2010, all rights reserved

What’s been learned? Quantitative analysis can determine the likelihood of overrunning the schedule Architectural weaknesses in the schedule are revealed and quantified Risks needed to balance investor commitment can be estimated ©Square Peg Consulting, 2010, all rights reserved

Adding quantitative risk analysis your Swiss Army Knife

by John Goodpasture

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