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Global Sensitivity Analysis of Predictor
           Models in Software Engineering

                                   Ste...
Introduction
Predictor Models in
Software
Engineering
Problem
Example:
Fischer-Wagner
Model
Questions About the
Model
Over...
Predictor Models in Software Engineering


                          Predictor models describe situations in software engi...
Problem


                          The models themselves can be complex
Introduction
                      s
Predictor Mo...
Example: Fischer-Wagner Model


                            Reliability model used at Siemens COM
Introduction
           ...
Questions About the Model


                          How do the input parameters influence the output?
Introduction
      ...
Overview

Introduction
                      Introduction
Predictor Models in
Software
                      Global Sensit...
Introduction
Global Sensitivity
Analysis
Definition
Method
Variance-based
Methods
Main Effect
Higher-Order Effects
Total Effec...
Definition

Introduction
                          Saltelli (2000): “Sensitivity analysis studies the relationships
       ...
Method

Introduction                Input                        Model                 Output
Global Sensitivity
Analysis
...
Method

Introduction                Input                        Model                 Output
Global Sensitivity
Analysis
...
Method

Introduction                Input                        Model                 Output
Global Sensitivity
Analysis
...
Method

Introduction                Input                        Model                 Output
Global Sensitivity
Analysis
...
Method

Introduction                Input                        Model                 Output
Global Sensitivity
Analysis
...
Method

Introduction                Input                        Model                 Output
Global Sensitivity
Analysis
...
Method

Introduction                Input                        Model                 Output
Global Sensitivity
Analysis
...
Method

Introduction                Input                        Model                 Output
Global Sensitivity
Analysis
...
Method

Introduction                Input                        Model                 Output
Global Sensitivity
Analysis
...
Method

Introduction                Input                        Model                 Output
Global Sensitivity
Analysis
...
Method

Introduction                Input                        Model                 Output
Global Sensitivity
Analysis
...
Variance-based Methods


                          Global analysis usually variance-based
Introduction
                   ...
Variance-based Methods


                          Global analysis usually variance-based
Introduction
                   ...
Main Effect

Introduction
                      Decomposition of the variance V of f (x)
Global Sensitivity
Analysis
      ...
Higher-Order Effects


                      Higher-order indices analog
Introduction
Global Sensitivity
Analysis
         ...
Total Effect


                          Sum of the first- and higher-order effects of xi
Introduction
                      ...
Total Effect


                          Sum of the first- and higher-order effects of xi
Introduction
                      ...
Total Effect


                          Sum of the first- and higher-order effects of xi
Introduction
                      ...
Total Effect


                          Sum of the first- and higher-order effects of xi
Introduction
                      ...
Total Effect


                          Sum of the first- and higher-order effects of xi
Introduction
                      ...
Total Effect


                          Sum of the first- and higher-order effects of xi
Introduction
                      ...
Total Effect


                          Sum of the first- and higher-order effects of xi
Introduction
                      ...
Total Effect


                          Sum of the first- and higher-order effects of xi
Introduction
                      ...
Introduction
Global Sensitivity
Analysis

Approach for SE
Overview of the
Approach
Determining
Distributions
Example:
Dist...
Overview of the Approach

Introduction
                                                                    Global
Global S...
Determining Distributions


                         Distribution of the values of the input parameteters
Introduction
   ...
Example: Distributions


                         Based on expert opinion
Introduction
                     s
Global Sensi...
Visualising Using Scatterplots


                         Sampling using the distributions
Introduction
                  ...
p1 and µ

                       900
Introduction
Global Sensitivity
Analysis               800
Approach for SE
          ...
d and µ

                         900
Introduction
Global Sensitivity
Analysis                 800
Approach for SE
       ...
t and µ

                         900
Introduction
Global Sensitivity
                         800
Analysis

Approach for ...
inf and µ

                         900
Introduction
Global Sensitivity
Analysis                 800
Approach for SE
     ...
Applying Global SA


                         Various methods for calculating indices
Introduction
                     s
...
Indizes


                     Main Effect
Introduction
Global Sensitivity
Analysis
                                  t    ...
Indizes


                     Main Effect
Introduction
Global Sensitivity
Analysis
                                    t  ...
Introduction
Global Sensitivity
Analysis

Approach for SE

Summary
Conclusions




                                  Summa...
Conclusions


                         Sensitivity analysis useful tool for predictor models
Introduction
                ...
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Global Sensitivity Analysis of Predictor Models in Software Engineering

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Transcript of "Global Sensitivity Analysis of Predictor Models in Software Engineering"

  1. 1. Global Sensitivity Analysis of Predictor Models in Software Engineering Stefan Wagner Software & Systems Engineering Technische Universit¨t M¨nchen a u Germany wagnerst@in.tum.de May 20, 2007 Dr. Stefan Wagner, TU M¨nchen u PROMISE – May 20, 2007 – 1 / 27
  2. 2. Introduction Predictor Models in Software Engineering Problem Example: Fischer-Wagner Model Questions About the Model Overview Introduction Global Sensitivity Analysis Approach for SE Summary Dr. Stefan Wagner, TU M¨nchen u PROMISE – May 20, 2007 – 2 / 27
  3. 3. Predictor Models in Software Engineering Predictor models describe situations in software engineering Introduction s Predictor Models in Various types, aims, . . . Software s Engineering Examples s Problem Example: Fischer-Wagner COCOMO (costs) x Model Questions About the Musa-Okumoto (reliability) x Model Overview Fault-proneness x Global Sensitivity Analysis Approach for SE Summary Dr. Stefan Wagner, TU M¨nchen u PROMISE – May 20, 2007 – 3 / 27
  4. 4. Problem The models themselves can be complex Introduction s Predictor Models in Their use needs a lot of effort Software s Engineering How can I analyse those models themeselves? s Problem Example: How can I simplify them? s Fischer-Wagner Model How do I improve their predictive power? s Questions About the Model Overview Global Sensitivity Analysis Approach for SE Summary Dr. Stefan Wagner, TU M¨nchen u PROMISE – May 20, 2007 – 4 / 27
  5. 5. Example: Fischer-Wagner Model Reliability model used at Siemens COM Introduction s Predictor Models in Two parameters estimated by failure data Software s Engineering Failure probability of a fault: pa = p1 · d(a−1) s Problem Example: Geometrical distribution : Fa (t) = 1 − (1 − pa )t s Fischer-Wagner Model Cummulated failures up to t: s Questions About the Model µ(t) = ∞ 1 − (1 − p1 · d(a−1) ) Overview a=1 Input parameters s Global Sensitivity Analysis p1 : Highest failure probability of a fault x Approach for SE d: Complexity of the system ]0; 1[ x Summary t: Execution time (incidents) x inf : approximation of ∞ x Output: µ(t) s More details: S. Wagner, H. Fischer. Ada-Europe, 2006 Dr. Stefan Wagner, TU M¨nchen u PROMISE – May 20, 2007 – 5 / 27
  6. 6. Questions About the Model How do the input parameters influence the output? Introduction s Predictor Models in Which parameter(s) do I have to estimate best to get a good Software s Engineering prediction? Problem Example: Are there insignificant parameters that I can remove? s Fischer-Wagner Model Questions About the Model Overview Global Sensitivity Analysis Approach for SE Summary Dr. Stefan Wagner, TU M¨nchen u PROMISE – May 20, 2007 – 6 / 27
  7. 7. Overview Introduction Introduction Predictor Models in Software Global Sensitivity Analysis Engineering Problem Example: Approach for SE Fischer-Wagner Model Summary Questions About the Model Overview Global Sensitivity Analysis Approach for SE Summary Dr. Stefan Wagner, TU M¨nchen u PROMISE – May 20, 2007 – 7 / 27
  8. 8. Introduction Global Sensitivity Analysis Definition Method Variance-based Methods Main Effect Higher-Order Effects Total Effect Global Sensitivity Analysis Approach for SE Summary Dr. Stefan Wagner, TU M¨nchen u PROMISE – May 20, 2007 – 8 / 27
  9. 9. Definition Introduction Saltelli (2000): “Sensitivity analysis studies the relationships s Global Sensitivity between information flowing in and out of the model.” Analysis Definition How do the input parameters influence the output? s Method How can this influence by quantified? Variance-based s Methods Global properties s Main Effect Higher-Order Effects Inclusion of influence of shape and scale x Total Effect Approach for SE Multidimensional averaging x Summary Dr. Stefan Wagner, TU M¨nchen u PROMISE – May 20, 2007 – 9 / 27
  10. 10. Method Introduction Input Model Output Global Sensitivity Analysis Definition x1 Method Variance-based Methods Main Effect Higher-Order Effects x2 Total Effect Approach for SE Summary Y f (x) x3 xn (Based on slide of S. Tarantola) Dr. Stefan Wagner, TU M¨nchen u PROMISE – May 20, 2007 – 10 / 27
  11. 11. Method Introduction Input Model Output Global Sensitivity Analysis Definition x1 Method Variance-based Methods Main Effect Higher-Order Effects x2 Total Effect Approach for SE Summary Y f (x) x3 xn (Based on slide of S. Tarantola) Dr. Stefan Wagner, TU M¨nchen u PROMISE – May 20, 2007 – 10 / 27
  12. 12. Method Introduction Input Model Output Global Sensitivity Analysis Definition x1 Method Variance-based Methods Main Effect Higher-Order Effects x2 Total Effect Approach for SE Summary Y f (x) x3 xn (Based on slide of S. Tarantola) Dr. Stefan Wagner, TU M¨nchen u PROMISE – May 20, 2007 – 10 / 27
  13. 13. Method Introduction Input Model Output Global Sensitivity Analysis Definition x1 Method Variance-based Methods Main Effect Higher-Order Effects x2 Total Effect Approach for SE Summary Y f (x) x3 xn (Based on slide of S. Tarantola) Dr. Stefan Wagner, TU M¨nchen u PROMISE – May 20, 2007 – 10 / 27
  14. 14. Method Introduction Input Model Output Global Sensitivity Analysis Definition x1 Method Variance-based Methods Main Effect Higher-Order Effects x2 Total Effect Approach for SE Summary Y f (x) x3 xn (Based on slide of S. Tarantola) Dr. Stefan Wagner, TU M¨nchen u PROMISE – May 20, 2007 – 10 / 27
  15. 15. Method Introduction Input Model Output Global Sensitivity Analysis Definition x1 Method Variance-based Methods Main Effect Higher-Order Effects x2 Total Effect Approach for SE Summary Y f (x) x3 xn (Based on slide of S. Tarantola) Dr. Stefan Wagner, TU M¨nchen u PROMISE – May 20, 2007 – 10 / 27
  16. 16. Method Introduction Input Model Output Global Sensitivity Analysis Definition x1 Method Variance-based Methods Main Effect Higher-Order Effects x2 Total Effect Approach for SE Summary Y f (x) x3 xn (Based on slide of S. Tarantola) Dr. Stefan Wagner, TU M¨nchen u PROMISE – May 20, 2007 – 10 / 27
  17. 17. Method Introduction Input Model Output Global Sensitivity Analysis Definition x1 Method Variance-based Methods Main Effect Higher-Order Effects x2 Total Effect Approach for SE Summary Y f (x) x3 xn (Based on slide of S. Tarantola) Dr. Stefan Wagner, TU M¨nchen u PROMISE – May 20, 2007 – 10 / 27
  18. 18. Method Introduction Input Model Output Global Sensitivity Analysis Definition x1 Method Variance-based Methods Main Effect Higher-Order Effects x2 Total Effect Approach for SE Summary Y f (x) x3 xn (Based on slide of S. Tarantola) Dr. Stefan Wagner, TU M¨nchen u PROMISE – May 20, 2007 – 10 / 27
  19. 19. Method Introduction Input Model Output Global Sensitivity Analysis Definition x1 Method Variance-based Methods Main Effect Higher-Order Effects x2 Total Effect Approach for SE Summary Y f (x) x3 xn (Based on slide of S. Tarantola) Dr. Stefan Wagner, TU M¨nchen u PROMISE – May 20, 2007 – 10 / 27
  20. 20. Method Introduction Input Model Output Global Sensitivity Analysis Definition x1 Method Variance-based Methods Main Effect Higher-Order Effects x2 Total Effect Approach for SE Summary Y f (x) x3 xn (Based on slide of S. Tarantola) Dr. Stefan Wagner, TU M¨nchen u PROMISE – May 20, 2007 – 10 / 27
  21. 21. Variance-based Methods Global analysis usually variance-based Introduction s Global Sensitivity “model-free” s Analysis Definition Analysis on the basis of sensitivity indices s Method Variance-based Main or first-order effect x Methods Main Effect x Higher-order effects Higher-Order Effects x Total effect Total Effect Approach for SE Decomposition in main effects and interactions s Summary k y = f (x) = f0 + fi (xi ) + fij (xi , xj ) i=1 i j>i + . . . + f1,2,...,k (x1 , x2 , . . . , xk ) Dr. Stefan Wagner, TU M¨nchen u PROMISE – May 20, 2007 – 11 / 27
  22. 22. Variance-based Methods Global analysis usually variance-based Introduction s Global Sensitivity “model-free” s Analysis Definition Analysis on the basis of sensitivity indices s Method Variance-based Main or first-order effect x Methods Main Effect x Higher-order effects Higher-Order Effects x Total effect Total Effect Approach for SE Decomposition in main effects and interactions s Summary For example k = 3: f (x) = f0 + f1 (x1 ) + f2 (x2 ) + f3 (x3 ) + f12 (x1 , x2 ) +f13 (x1 , x3 ) + f23 (x2 , x3 ) + f123 (x1 , x2 , x3 ) Dr. Stefan Wagner, TU M¨nchen u PROMISE – May 20, 2007 – 11 / 27
  23. 23. Main Effect Introduction Decomposition of the variance V of f (x) Global Sensitivity Analysis k Definition Var(y) = V = Vi + Vij Vijk + . . . + V1,2,...k Method Variance-based Methods i=1 i j i j k Main Effect Higher-Order Effects First-order sensitivity coefficient Total Effect Approach for SE Vi Si = Summary V (Factors Priorisation) Dr. Stefan Wagner, TU M¨nchen u PROMISE – May 20, 2007 – 12 / 27
  24. 24. Higher-Order Effects Higher-order indices analog Introduction Global Sensitivity Analysis Si1 ...io = Vi1 ...io /V Definition Method Variance-based Methods Main Effect Higher-Order Effects Total Effect Approach for SE With k = 4: Summary 2. order: S12 , S13 , S14 , S23 , S24 , S34 3. order: S123 , S124 , S134 , S234 4. order: S1234 Dr. Stefan Wagner, TU M¨nchen u PROMISE – May 20, 2007 – 13 / 27
  25. 25. Total Effect Sum of the first- and higher-order effects of xi Introduction s Global Sensitivity Removal of the non-relevant parts s Analysis Definition Method Variance-based S1 + S2 + S3 + S4 + S12 + S13 + S14 + S23 + S24 + S34 + Methods Main Effect S123 + S124 + S134 + S234 + S1234 = 1 Higher-Order Effects Total Effect Approach for SE Summary (Factors Fixing) Dr. Stefan Wagner, TU M¨nchen u PROMISE – May 20, 2007 – 14 / 27
  26. 26. Total Effect Sum of the first- and higher-order effects of xi Introduction s Global Sensitivity Removal of the non-relevant parts s Analysis Definition Method Variance-based S1 + //2 + S3 + S4 + S12 + S13 + S14 + S23 + S24 + S34 + S/ Methods Main Effect Higher-Order Effects S123 + S124 + S134 + S234 + S1234 = 1 Total Effect Approach for SE Summary (Factors Fixing) Dr. Stefan Wagner, TU M¨nchen u PROMISE – May 20, 2007 – 14 / 27
  27. 27. Total Effect Sum of the first- and higher-order effects of xi Introduction s Global Sensitivity Removal of the non-relevant parts s Analysis Definition Method Variance-based S1 + //2 + / 3 + S4 + S12 + S13 + S14 + S23 + S24 + S34 + S/ S // Methods Main Effect Higher-Order Effects S123 + S124 + S134 + S234 + S1234 = 1 Total Effect Approach for SE Summary (Factors Fixing) Dr. Stefan Wagner, TU M¨nchen u PROMISE – May 20, 2007 – 14 / 27
  28. 28. Total Effect Sum of the first- and higher-order effects of xi Introduction s Global Sensitivity Removal of the non-relevant parts s Analysis Definition Method Variance-based S1 + //2 + / 3 + /// + S12 + S13 + S14 + S23 + S24 + S34 + S/ S // S4 Methods Main Effect Higher-Order Effects S123 + S124 + S134 + S234 + S1234 = 1 Total Effect Approach for SE Summary (Factors Fixing) Dr. Stefan Wagner, TU M¨nchen u PROMISE – May 20, 2007 – 14 / 27
  29. 29. Total Effect Sum of the first- and higher-order effects of xi Introduction s Global Sensitivity Removal of the non-relevant parts s Analysis Definition Method Variance-based S1 + //2 + / 3 + /// + S12 + S13 + S14 + S23 + S24 + S34 + S/ S // S4 // // // // // // Methods Main Effect Higher-Order Effects S123 + S124 + S134 + S234 + S1234 = 1 Total Effect Approach for SE Summary (Factors Fixing) Dr. Stefan Wagner, TU M¨nchen u PROMISE – May 20, 2007 – 14 / 27
  30. 30. Total Effect Sum of the first- and higher-order effects of xi Introduction s Global Sensitivity Removal of the non-relevant parts s Analysis Definition Method Variance-based S1 + //2 + / 3 + /// + S12 + S13 + S14 + S23 + S24 + S34 + S/ S // S4 // // // // // // Methods Main Effect Higher-Order Effects S123 + S124 + S134 + / 234 + S1234 = 1 S // // / Total Effect Approach for SE Summary (Factors Fixing) Dr. Stefan Wagner, TU M¨nchen u PROMISE – May 20, 2007 – 14 / 27
  31. 31. Total Effect Sum of the first- and higher-order effects of xi Introduction s Global Sensitivity Removal of the non-relevant parts s Analysis Definition Method Variance-based S1 + //2 + / 3 + /// + S12 + S13 + S14 + S23 + S24 + S34 + S/ S // S4 // // // // // // Methods Main Effect Higher-Order Effects S123 + S124 + S134 + / 234 + S1234 = 1 S // // / Total Effect Approach for SE ST 1 = S1 + S12 + S13 + S14 + S123 + S124 + S134 + S1234 Summary (Factors Fixing) Dr. Stefan Wagner, TU M¨nchen u PROMISE – May 20, 2007 – 14 / 27
  32. 32. Total Effect Sum of the first- and higher-order effects of xi Introduction s Global Sensitivity Removal of the non-relevant parts s Analysis Definition Method Variance-based S1 + //2 + / 3 + /// + S12 + S13 + S14 + S23 + S24 + S34 + S/ S // S4 // // // // // // Methods Main Effect Higher-Order Effects S123 + S124 + S134 + / 234 + S1234 = 1 S // // / Total Effect Approach for SE ST 1 = S1 + S12 + S13 + S14 + S123 + S124 + S134 + S1234 Summary ST 2 = S2 + S12 + S23 + S24 + S123 + S124 + S234 + S1234 (Factors Fixing) Dr. Stefan Wagner, TU M¨nchen u PROMISE – May 20, 2007 – 14 / 27
  33. 33. Introduction Global Sensitivity Analysis Approach for SE Overview of the Approach Determining Distributions Example: Distributions Approach for SE Visualising Using Scatterplots p1 and µ d and µ t and µ inf and µ Applying Global SA Indizes Summary Dr. Stefan Wagner, TU M¨nchen u PROMISE – May 20, 2007 – 15 / 27
  34. 34. Overview of the Approach Introduction Global Global Sensitivity Visualising Determining Analysis sensitivity using distributions Approach for SE analyses scatterplots Overview of the Approach Determining Distributions Example: Distributions Visualising Using Scatterplots .375 p1 and µ .045 d and µ .003 t and µ .002 inf and µ Input Sensitivity Applying Global SA Scatterplots distributions indices Indizes Summary Dr. Stefan Wagner, TU M¨nchen u PROMISE – May 20, 2007 – 16 / 27
  35. 35. Determining Distributions Distribution of the values of the input parameteters Introduction s Global Sensitivity Derived from s Analysis Approach for SE scientific literature x Overview of the Approach physical boundaries x Determining expert opinion x Distributions Example: surveys x Distributions Visualising Using experiments x Scatterplots p1 and µ d and µ t and µ inf and µ Applying Global SA Indizes Summary Dr. Stefan Wagner, TU M¨nchen u PROMISE – May 20, 2007 – 17 / 27
  36. 36. Example: Distributions Based on expert opinion Introduction s Global Sensitivity General parameter s Analysis Approach for SE p1 uniformly distributed between 0 and 1 x Overview of the Approach d uniformly distributed between 0.9 and 1 x Determining Distributions Dependent on application s Example: Distributions Visualising Using inf e.g.. uniformly distributed between 50 and 500 x Scatterplots p1 and µ For t e.g. t ∼ N (1000, 200) x d and µ t and µ inf and µ Applying Global SA Indizes Summary Dr. Stefan Wagner, TU M¨nchen u PROMISE – May 20, 2007 – 18 / 27
  37. 37. Visualising Using Scatterplots Sampling using the distributions Introduction s Global Sensitivity Pairwise relationship between factors s Analysis Detection of errors in the model s Approach for SE Overview of the Indications of influences s Approach Determining Distributions Example: Distributions Visualising Using Scatterplots p1 and µ d and µ t and µ inf and µ Applying Global SA Indizes Summary Dr. Stefan Wagner, TU M¨nchen u PROMISE – May 20, 2007 – 19 / 27
  38. 38. p1 and µ 900 Introduction Global Sensitivity Analysis 800 Approach for SE 700 Overview of the Approach Determining 600 Distributions Example: µ 500 Distributions Visualising Using Scatterplots 400 p1 and µ d and µ 300 t and µ inf and µ 200 Applying Global SA Indizes 100 Summary 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 p1 Dr. Stefan Wagner, TU M¨nchen u PROMISE – May 20, 2007 – 20 / 27
  39. 39. d and µ 900 Introduction Global Sensitivity Analysis 800 Approach for SE 700 Overview of the Approach Determining 600 Distributions Example: 500 Distributions µ Visualising Using Scatterplots 400 p1 and µ d and µ 300 t and µ inf and µ 200 Applying Global SA Indizes 100 Summary 0 0.9 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1 d Dr. Stefan Wagner, TU M¨nchen u PROMISE – May 20, 2007 – 21 / 27
  40. 40. t and µ 900 Introduction Global Sensitivity 800 Analysis Approach for SE 700 Overview of the Approach 600 Determining Distributions Example: 500 Distributions µ Visualising Using 400 Scatterplots p1 and µ 300 d and µ t and µ 200 inf and µ Applying Global SA 100 Indizes Summary 0 99200 99400 99600 99800 100000 100200 100400 100600 100800 t Dr. Stefan Wagner, TU M¨nchen u PROMISE – May 20, 2007 – 22 / 27
  41. 41. inf and µ 900 Introduction Global Sensitivity Analysis 800 Approach for SE 700 Overview of the Approach Determining 600 Distributions Example: 500 Distributions µ Visualising Using Scatterplots 400 p1 and µ d and µ 300 t and µ inf and µ 200 Applying Global SA Indizes 100 Summary 0 400 450 500 550 600 650 700 750 800 850 900 inf Dr. Stefan Wagner, TU M¨nchen u PROMISE – May 20, 2007 – 23 / 27
  42. 42. Applying Global SA Various methods for calculating indices Introduction s Global Sensitivity FAST (Fourier Amplitude Sensitivity Test) gives quantitative s Analysis results Approach for SE Overview of the Uses sampled data s Approach Determining Tool-support: Simlab s Distributions Example: Distributions Visualising Using Scatterplots p1 and µ d and µ t and µ inf and µ Applying Global SA Indizes Summary Dr. Stefan Wagner, TU M¨nchen u PROMISE – May 20, 2007 – 24 / 27
  43. 43. Indizes Main Effect Introduction Global Sensitivity Analysis t 6.88e-5 Approach for SE p1 0.0090 Overview of the Approach d 0.9026 Determining Distributions 0.0158 inf Example: Distributions Visualising Using Scatterplots p1 and µ d and µ t and µ inf and µ Applying Global SA Indizes Summary Dr. Stefan Wagner, TU M¨nchen u PROMISE – May 20, 2007 – 25 / 27
  44. 44. Indizes Main Effect Introduction Global Sensitivity Analysis t 6.88e-5 Approach for SE p1 0.0090 Overview of the Approach d 0.9026 Determining Distributions 0.0158 inf Example: Distributions Visualising Using Total Effect Scatterplots p1 and µ d and µ t 0.005788 t and µ p1 0.022365 inf and µ Applying Global SA d 0.975155 Indizes 0.086735 inf Summary Dr. Stefan Wagner, TU M¨nchen u PROMISE – May 20, 2007 – 25 / 27
  45. 45. Introduction Global Sensitivity Analysis Approach for SE Summary Conclusions Summary Dr. Stefan Wagner, TU M¨nchen u PROMISE – May 20, 2007 – 26 / 27
  46. 46. Conclusions Sensitivity analysis useful tool for predictor models Introduction s Global Sensitivity SA can help to s Analysis Approach for SE find errors in the models x Summary simplify the models x Conclusions identify interactions between input parameters x identify parameters that should be investigated more x get more robust predictions x Experience with s reliability model x QA economics model x process model x expert system for IT tools x Good tool-support available (Simlab: s http://simlab.jrc.cec.eu.int/) Dr. Stefan Wagner, TU M¨nchen u PROMISE – May 20, 2007 – 27 / 27
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