ATI's Quantitative Methods course: Bridging Project Management and System Engineering Technical Training Short Course

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This 3-day course is de¬signed for the professional program manager, system engineer, or project manager engaged in technically challenging projects where close technical collaboration between …

This 3-day course is de¬signed for the professional program manager, system engineer, or project manager engaged in technically challenging projects where close technical collaboration between engineering and management is a must. To that end, this course addresses major topics that bridge the disciplines of project management and system engineering. Each of the selected topics is presented from the perspective of quantitative methods. Students first learn a theory or narrative, and then related methods or practices. Ideas are demonstrated that are immediately applicable to programs and projects. Attendees receive a copy of the instructor’s text, Quantitative Methods in Project Management.

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  • 1. Video Sampler From ATI Professional Development Short Course Quantitative Methods: Bridging Project Management and System Engineering Instructor: John C. Goodpasture, PMPATI Course Schedule: http://www.ATIcourses.com/schedule.htmATIs Quantitative Methods: http://www.aticourses.com/Quantitative_Methods.htm
  • 2. www.ATIcourses.comBoost Your Skills 349 Berkshire Drive Riva, Maryland 21140with On-Site Courses Telephone 1-888-501-2100 / (410) 965-8805Tailored to Your Needs Fax (410) 956-5785 Email: ATI@ATIcourses.comThe Applied Technology Institute specializes in training programs for technical professionals. Our courses keep youcurrent in the state-of-the-art technology that is essential to keep your company on the cutting edge in today’s highlycompetitive marketplace. Since 1984, ATI has earned the trust of training departments nationwide, and has presentedon-site training at the major Navy, Air Force and NASA centers, and for a large number of contractors. Our trainingincreases effectiveness and productivity. Learn from the proven best.For a Free On-Site Quote Visit Us At: http://www.ATIcourses.com/free_onsite_quote.aspFor Our Current Public Course Schedule Go To: http://www.ATIcourses.com/schedule.htm
  • 3. Why number ideas are important for project management Cardinal Ordinal Deterministic Random• Metric • Rank choice • Numerical • Risk analysis calculation & priority reporting to • Calculations• Metric • Rank stakeholders and estimates reporting complexity • Population of random or• Budgets, sche • Give statistics probabilistic dules, resourc numerical quantities es visualization to position and rankCopyright 2011 Square Peg Consulting, LLC, All Rights Reserved 2
  • 4. Example: developer ranking of complexity Histogram of developer opinion Count [cardinal] 8 15 76th 30 Percentile 20 4 30 76% of rankings 15 are 4 or a 2 2 4 8 2 20 Rank [ordinal] • Minimum 2 • Maximum 8 • Median 5 3Copyright 2011 Square Peg Consulting, LLC, All Rights Reserved
  • 5. Comparison of deterministic and random numbers• Deterministic – Single point, one value – Certain knowledge 2 – Arithmetic on number values• Probabilistic, aka random – Range of possible values, with probabilities – Different values occur from one trial or instance to the next – Arithmetic on {value, value probability} pairs – Most useful for project management if distribution is stationary [invariant] with time and position 2.1 1 1.5 2 2.5 4Copyright 2011 Square Peg Consulting, LLC, All Rights Reserved 4
  • 6. Arithmetic operations with random numbers• Arithmetic operations require operations on distribution functions – Functional operations are often quite complex – Simulation methods substitute for direct calculations• As a practical matter, distributions are not often known – Only observations of distribution outcomes are known – Arithmetic operations applied to outcomes – Approximations are made using simpler functions as substitutes – Simulation methods derive estimators for actual—but unknown— functionsCopyright 2011 Square Peg Consulting, LLC, All Rights Reserved 5
  • 7. Logical operations with random numbers• UNION and INTERSECTION – Logical representation of addition and multiplication• Logic operations provide practical and useful approximations of outcomes Union or Summation A or B A+ B Intersection or Multiplication A and B A* BCopyright 2011 Square Peg Consulting, LLC, All Rights Reserved 6
  • 8. The Project Balance Sheet Tool Quantitative Methods in Project Management 7Copyright 2011 Square Peg Consulting, LLC, All Rights Reserved
  • 9. Recall the “Project Balance Sheet” Project Value from Project Estimate from the Top Down the Bottom Up Risk Investor Value Expectation & Resource Commitment Deliverables Cost Schedule Management investment Project employment of investment 8 Copyright 2011 Square Peg Consulting, LLC, All Rights Reserved
  • 10. Map from business to project1. Disaggregate sponsor needs: break down expectations, judgments, and commitments into component parts2. Categorize component parts into capacity, capability, resource needs, and risk2. Re-integrate component parts to identify gaps and missing parts Resource Sponsor Capacity Capability Risk Needs Expectations Resources, sk Schedule ills, commitm Feature X ent All the Value features and Cost judgments functions of widget A Environment, Dollars and Resource tools People, proce schedule Commitment ss, tools 9Copyright 2011 Square Peg Consulting, LLC, All Rights Reserved
  • 11. Plot confidence in cost [or schedule] Confidence that the $_amount will not be exceeded Likely RiskVery High High Medium Low Not to exceed cost $450K $475K $550K >$550K 10 Copyright 2011 Square Peg Consulting, LLC, All Rights Reserved
  • 12. Plot timeline of project expense and business value Business value Project Business value expenses from sales $450K $550K 11 Copyright 2011 Square Peg Consulting, LLC, All Rights Reserved
  • 13. Sampling Metrics for Project Estimates Quantitative Methods in Project ManagementCopyright 2011 Square Peg Consulting, LLC, All Rights Reserved 12
  • 14. In the beginning, there is a population • All the data values, events, or event Population outcomes that share a common situation or environment • Space that holds all the values of the Population space population • May be deterministic or the outcome of a Population values random process in/of the population • Only those populations that bear upon Population project results are important importance • Because a population bears upon project results, the population is importantCopyright 2011 Square Peg Consulting, LLC, All Rights Reserved 13
  • 15. Sampling risks Accuracy Completeness• Misunderstood • Excluded clusters or strata exclusions, clusters, or strata • Unrepresentative data quality• Unrepresentative sample data or deficiency value outliersCopyright 2011 Square Peg Consulting, LLC, All Rights Reserved 14
  • 16. Two risk assessments to be made Margin of error Confidence interval Estimated error around the Interval that probably contains the measurement, observation, or true population parameter calculation of statistics Confidence expresses probabilityInterval of possible values for the that the true parameter is in the statistic relative to the statistic intervalCopyright 2011 Square Peg Consulting, LLC, All Rights Reserved 15
  • 17. Margin of error exampleMargin of error % = 3 / 18 (x100) = 16.7% 18 Statistic 17 Sample Interval of statistic values: 3 20 ½ Interval Margin of error % = +/- 1.5 / 18 (x100) = +/- 8.3%Copyright 2011 Square Peg Consulting, LLC, All Rights Reserved 16
  • 18. Confidence interval• For some probability—for example, 95%--the true population statistic is within the interval – 5% of the trials may not have intervals that contain the true population – For a single trial, there is a 95% confidence that the true population statistic is within the sample interval For 95/100 trials Sample interval contains the true population statistics For 1 trial 5% chance the interval does not contain the true population statistics 18 Statistic Sample Interval of statistic: 3 17 20Copyright 2011 Square Peg Consulting, LLC, All Rights Reserved 17
  • 19. Confidence interval for proportional data Interval = p +/- Z * [p * (1 - p) / N] Where Z is range value of standard Normal distribution Z is normalized to the standard deviation Z = 1 means 1 σ from the mean Z rangeCopyright 2011 Square Peg Consulting, LLC, All Rights Reserved 18
  • 20. Margin of error, proportional data +/- Margin of Error = ½ Interval width / p Where ½ Interval width = +/- Z * [p * (1 - p) / N] Z = 1.96Copyright 2011 Square Peg Consulting, LLC, All Rights Reserved 19
  • 21. Hypothesis Testing Quantitative Methods in Project ManagementCopyright 2011 Square Peg Consulting, LLC, All Rights Reserved 20
  • 22. What if …. ?Design parameter change – You change a system design parameter with an expectation that there will be a difference in performance. – Comparing the ‘before’ to the ‘after’, is the difference a matter of chance, or has there been a systemic change in performance?Copyright 2011 Square Peg Consulting, LLC, All Rights Reserved 21
  • 23. Distributions of X and Y Sample X Sample YCopyright 2011 Square Peg Consulting, LLC, All Rights Reserved 22
  • 24. • We don’t know the distributions of sample X and sample Y (usually) – Not needed for hypothesis test – Distributions of sample average are known approximately Sample average distribution Sample X Sample YCopyright 2011 Square Peg Consulting, LLC, All Rights Reserved 23
  • 25. • H0 likely TRUE for difference values < 0.219• Otherwise, likely FALSE• With confidence of 95% H0 distribution & confidence curveCopyright 2011 Square Peg Consulting, LLC, All Rights Reserved 24
  • 26. Risk mitigation in time and resource schedules Quantitative Methods in Project ManagementCopyright 2011 Square Peg Consulting, LLC, All Rights Reserved 25
  • 27. Any issues?Should you be equally confident of making the milestone? Tandem path primitive Parallel path primitiveCopyright 2011 Square Peg Consulting, LLC, All Rights Reserved 26
  • 28. Interpreting the Confidence “S” CurveA. 68% confidence: value between -1 to +1B. 16% confidence: value > 1C. 84% confidence: value < 1 B 1 0.84 0.75 0.5 A 0.25 0.16 C 0 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 C A BCopyright 2011 Square Peg Consulting, LLC, All Rights Reserved 27
  • 29. Schedule example for tandem tasksSchedule network primitive Task duration distribution, D Task Probability distribution 0.45 0.4 Task A Task B 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 1 2 3 4 5 6 Duration range 1 - 6Copyright 2011 Square Peg Consulting, LLC, All Rights Reserved 28
  • 30. Milestone accumulates task performance Milestone Expected Value = 3.5 + 3.5 0.3 0.25 0.2 0.15 0.1 0.05 0 1 2 3 4 5 6 7 8 9 10 11 12 Milestone range 1 - 12Copyright 2011 Square Peg Consulting, LLC, All Rights Reserved 29
  • 31. Confidence for “schedule-at-mode” Date 1/1 1/21 2/12 3/15 3/25 1.2 Low confidence in 3/25 1 p/v 0.8 Calculate Confidence 0.6 0.4 0.2 0.0 0.5 0 1-Apr 2-Apr 4-Apr 23-Mar 24-Mar 25-Mar 26-Mar 27-Mar 28-Mar 29-Mar 30-Mar 3-Apr 5-Apr 31-MarCopyright 2011 Square Peg Consulting, LLC, All Rights Reserved 30
  • 32. Parallel path primitive What is the schedule confidence at the milestone? Distribution of tasks 0.45 0.4 0.35 0.3 0.25 0.2 Confidence: 80% at 4 1.2 0.15 0.1 1 0.05 0.8 0 1 2 3 4 5 6 0.6 0.4 0.2 0 1 2 3 4 5 6Copyright 2011 Square Peg Consulting, LLC, All Rights Reserved 31
  • 33. “Critical Chain” buffers uncertainty 1 2 10 days 11 days 12 days Buffer Project Buffer Path buffer mitigates 15 days 10 days “shift right” at the milestone of joining path Task on the critical path Task with risky duration, not on critical pathCritical chain is a concept developed in the bookCritical Chain (Goldratt, 1997) Copyright 2011 Square Peg Consulting, LLC, All Rights Reserved 32
  • 34. To learn more please attend ATI courseQuantitative Methods: Bridging Project Management and System Engineering Please post your comments and questions to our blog: http://www.aticourses.com/blog/ Sign-up for ATIs monthly Course Schedule Updates : http://www.aticourses.com/email_signup_page.html