| Preface | p. v |
| Acknowledgments | p. vii |
| Introduction and Overview | p. 1 |
| What is Software Engineering? | p. 1 |
| Uncertainty in Software Production | p. 2 |
| The Software Development Process | p. 2 |
| Sources of Uncertainty in the Development Process | p. 3 |
| The Quantification of Uncertainty | p. 4 |
| Probability as an Approach for Quantifying Uncertainty | p. 4 |
| Interpretations of Probability | p. 6 |
| Interpreting Probabilities in Software Engineering | p. 9 |
| The Role of Statistical Methods in Software Engineering | p. 9 |
| Chapter Summary | p. 11 |
| Foundational Issues: Probability and Reliability | p. 13 |
| Preamble | p. 13 |
| The Calculus of Probability | p. 14 |
| Notation and Preliminaries | p. 14 |
| Conditional Probabilities and Conditional Independence | p. 16 |
| The Calculus of Probability | p. 17 |
| The Law of Total Probability, Bayes' Law, and the Likelihood Function | p. 20 |
| The Notion of Exchangeability | p. 25 |
| Probability Models and Their Parameters | p. 28 |
| What is a Software Reliability Model? | p. 28 |
| Some Commonly Used Probability Models | p. 29 |
| Moments of Probability Distributions and Expectation of Random Variables | p. 39 |
| Moments of Probability Models: The Mean Time to Failure | p. 41 |
| Point Processes and Counting Process Models | p. 41 |
| The Nonhomogeneous Poisson Process Model | p. 43 |
| The Homogeneous Poisson Process Model | p. 45 |
| Generalizations of the Point Process Model | p. 46 |
| Fundamentals of Reliability | p. 52 |
| The Notion of a Failure Rate Function | p. 53 |
| Some Commonly Used Model Failure Rates | p. 54 |
| Covariates in the Failure Rate Function | p. 57 |
| The Concatenated Failure Rate Function | p. 58 |
| Chapter Summary | p. 59 |
| Exercises for Chapter 2 | p. 61 |
| Models for Measuring Software Reliability | p. 67 |
| Background: The Failure of Software | p. 67 |
| The Software Failure Process and Its Associated Randomness | p. 68 |
| Classification of Software Reliability Models | p. 70 |
| Models Based on the Concatenated Failure Rate Function | p. 72 |
| The Failure Rate of Software | p. 72 |
| The Model of Jelinski and Moranda (1972) | p. 72 |
| Extensions and Generalizations of the Model by Jelinski and Moranda | p. 75 |
| Hierarchical Bayesian Reliability Growth Models | p. 76 |
| Models Based on Failure Counts | p. 77 |
| Time Dependent Error Detection Models | p. 77 |
| Models Based on Times Between Failures | p. 80 |
| The Random Coefficient Autoregressive Process Model | p. 80 |
| A Non-Gaussian Kalman Filter Model | p. 81 |
| Unification of Software Reliability Models | p. 82 |
| Unification via the Bayesian Paradigm | p. 83 |
| Unification via Self-Exciting Point Process Models | p. 84 |
| Other Approaches to Unification | p. 86 |
| An Adaptive Concatenated Failure Rate Model | p. 91 |
| The Model and Its Motivation | p. 92 |
| Properties of the Model and Interpretation of Model Parameters | p. 94 |
| Chapter Summary | p. 95 |
| Exercises for Chapter 3 | p. 97 |
| Statistical Analysis of Software Failure Data | p. 101 |
| Background: The Role of Failure Data | p. 101 |
| Bayesian Inference, Predictive Distributions, and Maximization of Likelihood | p. 103 |
| Bayesian Inference and Prediction | p. 104 |
| The Method of Maximum Likelihood | p. 105 |
| Application: Inference and Prediction Using Jelinski and Moranda's Model | p. 106 |
| Application: Inference and Prediction Under an Error Detection Model | p. 110 |
| Specification of Prior Distributions | p. 113 |
| Standard of Reference--Noninformative Priors | p. 114 |
| Subjective Priors Based on Elicitation of Specialist Knowledge | p. 115 |
| Extensions of the Elicitation Model | p. 117 |
| Example: Eliciting Priors for the Logarithmic-Poisson Model | p. 118 |
| Application: Failure Prediction Using Logarithmic-Poisson Model | p. 120 |
| Inference and Prediction Using a Hierarchical Model | p. 124 |
| Application to NTDS Data: Assessing Reliability Growth | p. 126 |
| Inference and Predictions Using Dynamic Models | p. 129 |
| Inference for the Random Coefficient Exchangeable Model | p. 131 |
| Inference for the Adaptive Kalman Filter Model | p. 141 |
| Inference for the Non-Gaussian Kalman Filter Model | p. 143 |
| Prequential Prediction, Bayes Factors, and Model Comparison | p. 145 |
| Prequential Likelihoods and Prequential Prediction | p. 146 |
| Bayes' Factors and Model Averaging | p. 148 |
| Model Complexity--Occam's Razor | p. 150 |
| Application: Comparing the Exchangeable, Adaptive, and Non-Gaussian Models | p. 151 |
| An Example of Reversals in the Prequential Likelihood Ratio | p. 153 |
| Inference for the Concatenated Failure Rate Model | p. 154 |
| Specification of the Prior Distribution | p. 155 |
| Calculating Posteriors by Markov Chain Monte Carlo | p. 157 |
| Testing Hypotheses About Reliability Growth or Decay | p. 159 |
| Application to System 40 Data | p. 160 |
| Chapter Summary | p. 164 |
| Exercises for Chapter 4 | p. 166 |
| Software Productivity and Process Management | p. 169 |
| Background: Producing Quality Software | p. 169 |
| A Growth-Curve Model for Estimating Software Productivity | p. 170 |
| The Statistical Model | p. 171 |
| Inference and Prediction Under the Growth-Curve Model | p. 174 |
| Application: Estimating Individual Software Productivity | p. 176 |
| The Capability Maturity Model for Process Management | p. 180 |
| The Conceptual Framework | p. 181 |
| The Probabilistic Approach for Hierarchical Classification | p. 183 |
| Application: Classifying a Software Developer | p. 186 |
| Chapter Summary | p. 188 |
| Exercises for Chapter 5 | p. 190 |
| The Optimal Testing and Release of Software | p. 191 |
| Background: Decision Making and the Calculus of Probability | p. 191 |
| Decision Making Under Uncertainty | p. 192 |
| Utility and Choosing the Optimal Decision | p. 194 |
| Maximization of Expected Utility | p. 194 |
| The Utility of Money | p. 195 |
| Decision Trees | p. 196 |
| Solving Decision Trees | p. 197 |
| Software Testing Plans | p. 198 |
| Examples of Optimal Testing Plans | p. 202 |
| One-Stage Testing Using the Jelinski-Moranda Model | p. 202 |
| One-and Two-Stage Testing Using the Model by Goel and Okumoto | p. 206 |
| One-Stage Lookahead Testing Using the Model by Goel and Okumoto | p. 211 |
| Fixed-Time Lookahead Testing for the Goel-Okumoto Model | p. 212 |
| One-Bug Lookahead Testing Plans | p. 214 |
| Optimality of One-Stage Look Ahead Plans | p. 215 |
| Application: Testing the NTDS Data | p. 216 |
| Chapter Summary | p. 217 |
| Exercises for Chapter 6 | p. 219 |
| Other Developments: Open Problems | p. 221 |
| Preamble | p. 221 |
| Dynamic Modeling and the Operational Profile | p. 222 |
| Martingales, Predictable Processes, and Compensators: An Overview | p. 222 |
| The Doob-Meyer Decomposition of Counting Processes | p. 224 |
| Incorporating the Operational Profile | p. 227 |
| Statistical Aspects of Software Testing: Experimental Designs | p. 228 |
| Inferential Issues in Random and Partition Testing | p. 229 |
| Comparison of Random and Partition Testing | p. 231 |
| Design of Experiments in Software Testing | p. 232 |
| Design of Experiments in Multiversion Programming | p. 236 |
| Concluding Remarks | p. 237 |
| The Integration of Module and System Performance | p. 238 |
| The Protocols of Control Flow and Data Flow | p. 239 |
| The Structure Function of Modularized Software | p. 242 |
| Appendices | p. 247 |
| Statistical Computations Using the Gibbs Sampler | p. 249 |
| An Overview of the Gibbs Sampler | p. 250 |
| Generating Random Variates--The Rejection Method | p. 253 |
| Examples: Using the Gibbs Sampler | p. 254 |
| Gibbs Sampling the Jelinski-Moranda Model | p. 254 |
| Gibbs Sampling the Hierarchical Model | p. 255 |
| Gibbs Sampling the Adaptive Kalman Filter Model | p. 256 |
| Gibbs Sampling the Non-Gaussian Kalman Filter Model | p. 258 |
| The Maturity Questionnaire and Responses | p. 261 |
| The Maturity Questionnaire | p. 261 |
| Binary (Yes, No) Responses to the Maturity Questionnaire | p. 265 |
| Prior Probabilities and Likelihoods | p. 266 |
| The Maturity Levels P(M[subscript i] M[subscript i-1]) | p. 266 |
| The Key Process Areas P(K[subscript ij]) and P(K[subscript ij] M[subscript i]) | p. 266 |
| The Likelihoods L(K[subscript ij]; R[superscript ij]) | p. 268 |
| References | p. 269 |
| Author Index | p. 283 |
| Subject Index | p. 287 |
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