Statistical Methods in Software Engineering

by Singpurwalla, Nozer D.; Wilson, Simon P.

• ISBN13: 9780387988238
• ISBN10: 0387988238
• Format: Hardcover
• Copyright: 1999-08-01
• Publisher: Springer Verlag

Summary

This book establishes a framework for dealing with uncertainties in software engineering, and for using quantitative measures for decision making in this context. It brings in perspective the large body of work having statistical content that is relevant to software engineering. The audience is computer scientists, software engineers, and reliability analysts, who have some exposure to probability and statistics. The content is pitched at a level that is appropriate for research workers in software reliability, and for graduate level courses in applied statistics computer science, operations research, and software engineering.

Author Biography

Nozer D. Singpurwalla is Professor of Operations Research and of Statistics at The George Washington University. Simon P. Wilson is a lecturer in the Statistics Department of Trinity College Dublin.

Table of Contents

Preface	v
Acknowledgments	vii
Introduction and Overview	1	(12)
What is Software Engineering?	1	(1)
Uncertainty in Software Production	2	(2)
The Software Development Process	2	(1)
Sources of Uncertainty in the Development Process	3	(1)
The Quatification of Uncertainty	4	(5)
Probability as an Approach for Quantifying Uncertainty	4	(2)
Interpretations of Probability	6	(3)
Interpreting Probabilities in Software Engineering	9	(1)
The Role of Statistical Methods in Software Engineering	9	(2)
Chapter Summary	11	(2)
Foundational Issues: Probability and Reliability	13	(54)
Preamble	13	(1)
The Calculus of Probability	14	(14)
Notation and Preliminaries	14	(2)
Conditional Probabilities and Conditional Independence	16	(1)
The Calculus of Probability	17	(3)
The Law of Total Probability, Bayes' Law, and the Likelihood Function	20	(5)
The Notion of Exchangeability	25	(3)
Probability Models and Their Parameters	28	(13)
What is a Software Reliability Model?	28	(1)
Some Commonly Used Probability Models	29	(10)
Moments of Probability Distributions and Expectation of Random Variables	39	(2)
Moments of Probability Models: The Mean Time to Failure	41	(1)
Point Processes and Counting Process Models	41	(11)
The Nonhomogeneous Poisson Process Model	43	(2)
The Homogeneous Poisson Process Model	45	(1)
Generalizations of the Point Process Model	46	(6)
Fundamentals of Reliability	52	(7)
The Notion of a Failure Rate Function	53	(1)
Some Commonly Used Model Failure Rates	54	(3)
Covariates in the Failure Rate Function	57	(1)
The Concatenated Failure Rate Function	58	(1)
Chapter Summary	59	(8)
Exercises for Chapter 2	61	(6)
Models for Measuring Software Reliability	67	(34)
Background: The Failure of Software	67	(5)
The Software Failure Process and Its Associated Randomness	68	(2)
Classification of Software Reliability Models	70	(2)
Models Based on the Concatenated Failure Rate Function	72	(5)
The Failure Rate of Software	72	(1)
The Model of Jelinski and Moranda (1972)	72	(3)
Extensions and Generalizations of the Model by Jelinski and Moranda	75	(1)
Hierarchical Bayesian Reliability Growth Models	76	(1)
Models Based on Failure Counts	77	(3)
Time Dependent Error Detection Models	77	(3)
Models Based on Times Between Failures	80	(2)
The Random Coefficient Autoregressive Process Model	80	(1)
A Non-Gaussian Kalman Filter Model	81	(1)
Unification of Software Reliability Models	82	(9)
Unification via the Bayesian Paradigm	83	(1)
Unification via Self-Exciting Point Process Models	84	(2)
Other Approaches to Unification	86	(5)
An Adaptive Concatenated Failure Rate Model	91	(4)
The Model and Its Motivation	92	(2)
Properties of the Model and Interpretation of Model Parameters	94	(1)
Chapter Summary	95	(6)
Exercises for Chapter 4	97	(4)
Statistical Analysis of Software Failure Data	101	(68)
Background: The Role of Failure Data	101	(2)
Bayesian Inference, Predictive Distributions, and Maximization of Likelihood	103	(10)
Bayesian Inference and Prediction	104	(1)
The Method of Maximum Likelihood	105	(1)
Application Inference and Prediction Using Jelinski and Moranda's Model	106	(4)
Application: Inference and Prediction Under an Error Detection Model	110	(3)
Specification of Prior Distributions	113	(11)
Standard of Reference---Noninformative Priors	114	(1)
Subjective Priors Based on Elicitation of Specialist Knowledge	115	(2)
Extensions of the Elicitation Model	117	(1)
Example: Eliciting Priors for the Logarithmic-Poisson Model	118	(2)
Application: Failure Prediction Using Logarithmic-Poisson Model	120	(4)
Inference and Prediction Using a Hierarchical Model	124	(5)
Application to NTDS Data: Assessing Reliability Growth	126	(3)
Inference and Predictions Using Dynamic Models	129	(16)
Inference for the Random Coefficient Exchangeable Model	131	(10)
Inference for the Adpative Kalman Filter Model	141	(2)
Inference for the Non-Gaussian Kalman Filter Model	143	(2)
Prequential Prediction, Bayes Factors, and Model Comparison	145	(9)
Prequential Likelihoods and Prequential Prediction	146	(2)
Bayes' Factors and Model Averaging	148	(2)
Model Complexity---Occam's Razor	150	(1)
Application: Comapring the Exchangeable, Adaptive, and Non-Gaussian Models	151	(2)
An Example of Reversals in the Prequential Likelihood Ratio	153	(1)
Inference for the Concatenated Failure Rate Model	154	(10)
Specification of the Prior Distribution	155	(2)
Calculating Posteriors by Markov Chain Monte Carlo	157	(2)
Testing Hypotheses About Reliability Growth or Decay	159	(1)
Application to System 40 Data	160	(4)
Chapter Summary	164	(5)
Exercises for Chapter 4	166	(3)
Software Productivity and Process Management	169	(22)
Background: Producing Quality Software	169	(1)
A Growth-Curve Model for Estimating Software Productivity	170	(10)
The Satistical Model	171	(3)
Inference and Prediction Under the Growth-Curve Model	174	(2)
Application: Estimating Individual Software Produtivity	176	(4)
The Capability Maturity Model for Process Management	180	(8)
The Conceptual Framework	181	(2)
The Probabilistic Approach for Hierarchical Classification	183	(3)
Application: Classying a Software Developer	186	(2)
Chapter Summary	188	(3)
Exercises for Chapter 5	190	(1)
The Optimal Testing and Release of Software	191	(30)
Background: Decision Making and the Calculus of Probability	191	(1)
Decision Making Under Uncertainty	192	(2)
Utility and Choosing the Optimal Decision	194	(2)
Maximization of Expected Utility	194	(1)
The Utility of Money	195	(1)
Decision Trees	196	(2)
Solving Decision Trees	197	(1)
Software Testing Plans	198	(4)
Examples of Optimal Testing Plans	202	(14)
One-Stage Testing Using the Jelinski-Moranda Model	202	(4)
One-and Two-Stage Testing Using the Model by Goel and Okumoto	206	(5)
One-Stage Lookahead Testing Using the Model by Goel and Okumoto	211	(1)
Fixed-Time Lookahead Testing for the Goel-Okumoto Model	212	(2)
One-Bug Lookahead Testing Plans	214	(1)
Optimality of One-Stage Look Ahead Plans	215	(1)
Application: Testing the NTDS Data	216	(1)
Chapter Summary	217	(4)
Exercises for Chapter 6	219	(2)
Other Developments: Open Problems	221	(1)
Preamble	221	(1)
Dynamic Modeling and the Operational Profile	222	(1)
Martingales, Predictable Processes, and Compensators: An Overview	222	(2)
The Doob-Meyer Decomposition of Counting Processes	224	(3)
Incorporating the Operational Profile	227	(1)
Statistical Aspects of Software Testing: Experimental Designs	228	(1)
Inferential Issues in Random and Partition Testing	229