Monte Carlo, Resampling, And Other Estimation Tricks. Mauricio Aguiar ti MÉTRICAS, President IFPUG Immediate Past President
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1 Monte Carlo, Resampling, And Other Estimation Tricks Mauricio Aguiar ti MÉTRICAS, President IFPUG Immediate Past President
2 Agenda Introduction A Simple Example Another Example An Alternative Do It Yourself Monte Carlo <2>
3 Introduction
4 Introduction Estimates Estimates are quantitative projections of project characteristics such as: Product Size Effort Schedule Quality <4>
5 Introduction Uncertainty and Monte Carlo There is a certain degree of uncertainty in the input parameters of an estimation model We want to know how uncertainty may affect results This can be accomplished with the Monte Carlo method <5>
6 Introduction Inputs to an Estimation Model Size (Function Points, etc.) Project and Product Characteristics Estimated Effort for Each Activity Etc. <6>
7 Introduction Modeling Uncertainty Allow inputs to vary according to specific statistical distributions Example: Size Normal Distribution 950 PF 1000 PF 1050 PF <7>
8 A Simple Example
9 A Simple Example - I Execute unit test and construction for 5 modules (classes, functions, subroutines...) Assume work will be done sequentially <9>
10 A Simple Example II The Problem The 100% probability schedule would be 48 days A shorter schedule with 90% probability would be better What would that schedule be? <10>
11 A Simple Example III Estimate Quality Distributions: Normal, Triangular, and Uniform Modeling uncertainty <11>
12 A Simple Example IV Monte Carlo Simulate the construction and unit test of the 5 modules times Let individual effort vary according to the corresponding distribution Assess total effort variation <12>
13 A Simple Example V Monte Carlo <13>
14 A Simple Example VI Histogram of Simulated Schedule <14>
15 A Simple Example VII Cumulative Frequency of Simulated Scheduled Schedule less or equal to 38 days with 90% probability <15>
16 A Simple Example VIII Questions Do the distributions used reflect reality? Is a shorter schedule as likely to occur as a longer one? <16>
17 A Simple Example IX Questions Distributions: Normal, Triangular, Uniform, and Lognormal <17>
18 A Simple Example X Questions Simulate construction and unit test times substituting the lognormal distribution for the normal distribution <18>
19 A Simple Example XI Questions <19>
20 A Simple Example XII Questions <20>
21 A Simple Example XIII Questions Schedule now is 39 days <21>
22 Another Example
23 Another Example I Productivity - 9 Projects Productivity in Hours/Function Points Note: Not real data <23>
24 Another Example II Estimation Error ((Estimated Actual)/Actual) * 100 Mean Relative Error <24>
25 Another Example III Effort Data The quality of effort data is often low How would error in effort data affect the estimate? <25>
26 Another Example IV Effort Data <26>
27 Another Example V Effort Data <27>
28 Another Example VI Effort Data Less than 40% error with 90% probability. Maximum 42%. <28>
29 An Alternative
30 Resampling - I The Idea Monte Carlo requires assumptions about the distributions Resampling is based on replicating a sample a large number of times with replacement Statistics based on resampling will approach true values as the number of samples grow Resampling is independent of distribution assumptions <30>
31 Resampling - II An Example Build a 95% confidence interval for COBOL productivity based on ISBSG V10 data The data: 615 projects, average productivity 20.5 H/FP, median productivity 11.9 H/FP <31>
32 Resampling - III Sampling Distribution: Mean, Median <32>
33 Resampling IV Sampling Distribution: Mean <33>
34 Resampling V Sampling Distribution: Mean <34>
35 Resampling - VI Sampling Distribution: Median <35>
36 Resampling - VI Sampling Distribution: Median <36>
37 Do It Yourself
38 Do It Yourself - I Simulating the Triangular Distribution <38>
39 Do It Yourself - II Simulating the Triangular Distribution <39>
40 Do It Yourself - III Simulating the Triangular Distribution Working with Excel VBA <40>
41 Do It Yourself - IV Simulating the Triangular Distribution <41>
42 Summary
43 Summary Monte Carlo and Resampling Monte Carlo helps to identify variation in the results as a function of the uncertainty in the inputs The choice of the correct statistical distribution is very important in Monte Carlo Resampling will work even when the distribution is unknown A lot can be done using Excel & VBA There are professional Monte Carlo tools (Crystal XLSim, etc.) <43>
44 Summary References Savage, Sam L., Decision Making with Insight XLSim 2.0 Mooney, C.Z. and Duval, R.D, Bootstrapping: A Nonparametric Approach to Statistical Inference, SAGE, 1993 Davidson, A.C. and Hinkley, D.V., Bootstrap Methods and Their Application, Cambridge University Press, 1997 <44>
45 Mauricio Aguiar ti MÉTRICAS <45>
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