1. 1 COCOMO II Integrated with Crystal Ball ® Risk Analysis Software Clate Stansbury MCR, LLC cstansbury@mcri.com (703) 506-4600 Prepared for 19 th International Forum on COCOMO Software Cost Modeling University of Southern California Los Angeles CA 26-29 October 2004

2. 2 Contents Purpose: Describing Uncertainty Representing Uncertain Inputs Simulating Costs Correlating Inputs and Costs Summary

3. 3 Estimators Must Describe Uncertainty Report Cost As a Statistical Quantity, Not a Point –Cost of Any Incomplete Program Is Uncertain –Estimator Must Report That Uncertainty as Part of His or Her Delivered Estimate Cost-risk Analysis Allows Estimator to Report Cost As a Probability Distribution, So Decision-maker Is Made Aware of –Expected Cost (Mean) –50 th Percentile Cost (Median) –80 th Percentile Cost –Overrun Probability of Project Budget

4. 4 Representing Uncertain Inputs Using Triangular Distributions

5. 5 Triangular Distribution of Element Cost, Reflecting Uncertainty in “Best” Estimate Optimistic Cost Best-Estimate Cost (Mode = Most Likely) Cost Implication of Technical, Programmatic Assessment

6. 6 COCOMO Cost Drivers as Triangular Distributions For Each COCOMO II Input … –Input Request Interpreted as a Triangular Distribution –User Estimates Optimistic, Most Likely, and Pessimistic Values (which may not always be all different from each other) Optimistic Pessimistic Most Likely (mode) Probability Cost User provides three values for each COCOMO II input, as though there were three separate projects.

7. 7 COCOMO Cost Drivers as Triangular Distributions 0.901.14

8. 8 COCOMO Cost Drivers as Triangular Distributions Why triangular distribution? Triangular Distribution is Simple and Malleable Parameters (Optimistic, Most Likely, Pessimistic) Are Easy to Define and Explain Could Have User Provide Parameters for Normal, Lognormal, Exponential, Uniform, or Beta Distributions, for Example, if More is known about the distributions Good Topic for Further Research….

9. 9 Processing Uncertainty Using Simulations

10. 10 How to Process Triangular Distributions? Taking the Product of Effort Multipliers When Each EM is a Triangular Distribution? How to Compute Rest of COCOMO II Algorithm? How to Sum Code Counts for All CSCIs?

11. 11 Traditional “Roll-Up” Method (Too Simple) Define “Best Estimate” of Each Cost Element to be the Most Likely Cost of that Element List Cost Elements in a Work-Breakdown Structure (WBS) –Calculate “Best Estimate” of Cost for Each Element –Sum All Best Estimates –Define Result to be “Best Estimate” of Total Project Cost Unfortunately, It Turns Out That Things are Not as Simple as They Seem – There are a Lot of Problems with This Approach

12. 12 Why “Roll-up” Doesn’t Work MERGE WBS-ELEMENT COST DISTRIBUTIONS INTO TOTAL-COST NORMAL DISTRIBUTION ROLL-UP OF MOST LIKELY WBS-ELEMENT COSTS MOST LIKELY TOTAL COST $ WBS-ELEMENT TRIANGULAR COST DISTRIBUTIONS...... $ $ $ Most Likely

13. 13 What Information a Cost Estimate Should Provide Statistical Information Output About the Cost –Probability Density (Frequency Distribution or Histogram) –S-curve (Cumulative Probability Distribution) –Percentiles –Min, Max, Mode, Mean

14. 14 What a Cost Estimate Should Look Like “S-Curve” “Density Curve” Frequency Chart.000.005.010.015.020 0 49.25 98.5 147.7 197 462.43537.16611.89686.62761.35 10,000 Trials 71 Outliers Forecast: A8 (Crystal Ball  Outputs)

15. 15 Cost-Risk Analysis Works by Simulating System Cost In Engineering Work, Computer Simulation of System Performance is Standard Practice, with Key Performance Characteristics Modeled by Monte Carlo Analysis as Random Variables, e.g. –Data Throughput –Time to Lock –Time Between Data Receipt and Delivery –Atmospheric Conditions Cost-Risk Analysis Enables the Cost Analyst to Conduct a Computer Simulation of System Cost –WBS-element Costs Are Modeled As Random Variables –Total System Cost Distribution is Determined by Monte Carlo Simulation –Cost is Treated as a Performance Criterion

16. 16 Crystal Ball  Risk- Analysis Software Commercially Available Third-Party Software Add-on to Excel, Marketed by Decisioneering, Inc., 2530 S. Parker Road, Suite 220, Aurora, CO 80014, (800) 289-2550 Inputs –Parameters Defining WBS-Element Distributions –Rank Correlations Among WBS-Element Cost Distributions Mathematics –Monte-Carlo (Random) or Latin Hypercube (Stratified) Statistical Sampling –Virtually All Probability Distributions That Have Names Can Be Used –Suggests Adjustments to Inconsistent Input Correlation Matrix Outputs –Percentiles and Other Statistics of Program Cost –Cost Probability Density and Cumulative Distribution Graphics

17. 17 How CB Simulations Work Trial 2Trial 5000Trial 1 =SUM($G$4:$G$8) Assumption Cell G5 Total Cost Forecast

18. 18 Representing Correlations Among Risks

19. 19 Risks are Correlated Resolving One WBS Element’s Risk Issues by Spending More Money on It Often Involves Increasing Cost of Several Other Elements as Well –For Example, Excessive Complexity in One CSCI Impacts Effort Required to Develop Other CSCIs that Interface with It –Schedule Slippage Due to Problems in One CSCI Lead to Cost Growth and Schedule Slippage in Other Elements (“Standing Army Effect”) –Hardware Problems Discovered Late in Program Often Have to Be Circumvented by Making Expensive Last-minute Fixes to the Software As We Will Soon See, Inter-Element Correlation Tends to Increase the Variance of the Total-Cost Probability Distribution Numerical Values of Inter-WBS-Element Correlations are Difficult to Estimate, but That’s Another Story

20. 20 Maximum Possible Underestimation of Total-Cost Sigma Percent Underestimated When Correlation Assumed to be 0 Instead of  (n=# of WBS elements)

21. 21 Selection of Correlation Values “Ignoring” Correlation Issue is Equivalent to Assuming that Risks are Uncorrelated, i.e., that All Correlations are Zero Square of Correlation (namely, R 2 ) Represents Percentage of Variation in one WBS Element’s Cost that is Attributable to Influence of Another’s Reasonable Choice of Nonzero Values Brings You Closer to Truth Most Elements are, in Fact, Pairwise Correlated 0.2 is at “Knee” of Curve on Previous Charts, thereby Providing Most of the Benefits at Least Commitment

22. 22 Determining Correlations Among COCOMO II Cost Drivers Default Correlations –Correlations of Intra-CSCI Inputs to Default to 0.5 –Correlations of Inter-CSCI Efforts to Default to 0.2 More Detailed Default Correlations? –Higher Correlation Between RELY and DOCU? –COCOMO II Security Extension Cost Driver Related to Existing Cost Drivers

23. 23 Summary Estimator Must Model Uncertainty Describe Uncertainty by Representing COCOMO Inputs as Triangular Distributions Calculate Implications of Uncertainty by Using Monte Carlo or Latin Hypercube Simulations to Perform COCOMO II Algorithm Consider Correlation Among CSCI Risks and Costs Professional Software, e.g., Crystal Ball, is Available to do Computations

24. 24 Acronyms AAAssessment and Assimilation ATAutomatically Translated code CBCrystal Ball CMPercent of Code Modified COCOMOConstructive Cost Model CSCIComputer Software Cost Integrator DMPercent of Design Modified EIExternal Input EIFExternal Interface File EOExternal Output EQExternal Inquiry ILFInternal Logical File IMEffort for Integration KSLOCThousands of Source Lines of Code MSMicrosoft O,M,POptimistic, Most Likely, Pessimistic SCEDSchedule compression/expansion rating SLOCSource Lines of Code SUSoftware UFPUnadjusted Function Point UNFMProgrammer Unfamiliarity rating USCUniversity of Southern California WBSWork Breakdown Structure

25. 25 Backup Slides

26. 26 Correlation Matters Suppose for Simplicity –There are n Cost Elements –Each –Each Corr(C i,C j ) =  < 1 –Total Cost  VarC i  2

27. 27 Cost Estimate Frequency Chart Approximation of Cost-Probability Distribution Effort

28. 28 Cost Estimate Cumulative-Probability Function Probability of Cost Being Less Than x Effort

29. 29 Statistical Information Trials1500 Mean190.12 Median 189.36 Mode--- Standard Deviation13.96 Variance195.01 Skewness0.15 Kurtosis 2.84 Coeff. of Variability0.07 Range Minimum152.86 Range Maximum237.42 Range Width84.56 Mean Std. Error 0.36 Cost Estimate Statistics PercentileEffort 55%191.11 60%193.12 65%195.36 70%197.51 75%199.69 80%202.34 85%204.86 90%208.09 95%213.71 100%237.42 PercentileEffort 0%152.86 5%167.41 10%171.84 15%175.86 20%178.55 25%180.77 30%182.66 35%184.49 40%185.99 45%187.57 50%189.36 Confidence Levels

30. 30 Correlation Matrices Allow User to Adjust Correlations One Matrix for Each CSCI Allows Estimator to Set Correlations Among Cost Drivers for that CSCI