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On Representing Uncertainty In Some COCOMO Model Family Parameters October 27, 2004 John Gaffney j.gaffney@lmco.com 301-240-7038 Fellow, Software & Systems Resource Center, Lockheed Martin

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(c) Copyright, Lockheed Martin Corporation, 2004 2 Background Uncertainties should be recognized in estimates of effort/cost, schedule, and other measures of interest in software and systems development. Managers and technical personnel need to make tradeoffs and decisions under uncertainty through the effective assessment and evaluation of risks. All too often, “the” value is presented, unaccompanied by any statement of the degree of uncertainty in that value. –Program managers and others involved in developing estimates for proposals should be able to quantify the degree of uncertainty in the estimates that they produce. –Estimating cost, schedule, and other product or process variables as single numbers fails to provide decision makers with information sufficient to make good bidding and other decisions. Suggestion: Develop estimate of RISK for the value of the parameter of interest (e.g., COSYSMO size drivers, development effort) –Risk: A measure of the probability of an undesirable situation.

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(c) Copyright, Lockheed Martin Corporation, 2004 3 Overview A method, prototype tools, and example applications are presented for explicitly dealing with and quantifying uncertainty in the values of various parameters used in COSYSMO and COCOMO II. They should be usable in other members of the COCOMO family of estimation models as well. The uncertainty is defined in terms of an empirical probability distribution for the value of the parameter of interest and one minus its value or the “risk.”Examples: –Cost Risk= Probability that the target value for the cost (or effort) will be exceeded. –Schedule Risk= Probability that the target value for the schedule (duration) will be exceeded. In general, if higher values (such as a prospective cost, or cost driver) are less desirable, then the risk is the probability that the target value will be exceeded. However, if higher values are more desirable (such as Mean-Time-Between- Failures), then the risk is the probability that the actual value will be less than the target value. The Pearson-Tukey three-point approximation is used for estimating the probability distribution for each parameter whose variation is represented. The three points use values at the (estimated) 5%,50%, and 95% fractiles. –Values obtained by expert opinion, experience data, or a combination of them; base on an assessment of impact of “risk factors.”

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(c) Copyright, Lockheed Martin Corporation, 2004 4 COSYSMO Size Driver Prototype Excel-based prototype tool. Provides cumulative probability and risk distributions for COSYSMO size,S. S=Σ(w i *s i ); i=1,2,3,4. The w i are weights for “easy,” “normal,” and “difficult.” The S i, sizes, are: # of system requirements, # of system interfaces, # of operational scenarios, and # of critical algorithms.

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(c) Copyright, Lockheed Martin Corporation, 2004 5 Example, Illustrative Application of COSYSMO Prototype

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(c) Copyright, Lockheed Martin Corporation, 2004 6

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9 COCOMO II “Risk” Prototype, page 1 of 2 An excel-based prototype tool was developed to demonstrate the concept of identifying the uncertainty in COCOMO II cost drivers and in the values of three other parameters of the equation that estimates person months (PM). The tool estimates two principal components:: –The range for the product of 4 cost driver values –The range of values of person months, based on the uncertainties in the cost driver product (D),the size (S), the size exponent (E), and the multiplying constant (A): PM=A*S E *D. The tool illustrates the possible range of uncertainty for 4 Early Design Model cost drivers, and for D, their product, which would include other drivers in an actual case: –RCPX: Product Reliability and Complexity –PERS: Personnel Capability –PREX: Personnel Experience –FCIL: Facilities The coverage of the prototype could be expanded to explicitly handle more than 4 cost drivers and of course, other drivers could be chosen and a more nearly complete risk assessment made.

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(c) Copyright, Lockheed Martin Corporation, 2004 10 COCOMO II “Risk” Prototype, page 2 of 2 Range of values provided for Person Months, PM: PM=A*(S E )*D where: PM=Person Months, S=Size (KSLOC); E=exponent; D=Product of Cost Drivers. –Three-point distribution estimates provided for:A,S,E, and D (obtained from the excel tool that develops the distribution of the product of 4 drivers. –The two tool sheets are linked together. The Pearson-Tukey three-point approximation for each parameter (and for each of the four cost drivers) is used. –The three points use values at the (estimated) 5%,50%, and 95% fractiles. –Values obtained by expert opinion, experience data, or combination.

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(c) Copyright, Lockheed Martin Corporation, 2004 11 Example, Illustrative Application of COCOMO II Prototype

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(c) Copyright, Lockheed Martin Corporation, 2004 18 Some References 1.In Chapter 8, How To Estimate Software Cost, in The Software Measurement Guidebook, by J. Gaffney, R. Cruickshank et al., Thomson Computer Press, 1995. 2.In the section, How to Estimate Software Project Schedules, by J. Gaffney, in the book, Software Engineering Project Management, edited by Richard Thayer, IEEE Computer Press, 1997. 3.Software Risk Metrics and Tool, by J. Ulvila, J. Gaffney, and J. Chinnis, Metrics 2002, IEEE 8 th International Symposium on Software Metrics. 4.A Methodology and Implementation For Software System Cost and Risk Estimation, by J. Gaffney, J. Bridel, and D. McGovern, 8 th PSM Users’ Group Conference, July, 2004.

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