Recurrent event modeling based on the Yule process : application to water network asset management / Yves Le Gat.

Format:

Book

Author/Creator:

Le Gat, Yves, author.

Series:

Mathematics and Statistics Series. Mathematical Models and Methods in Reliability Set ; Volume 2

Language:

English

Subjects (All):

Reliability (Engineering)--Mathematical models.

Reliability (Engineering).

Stochastic processes.

Water-pipes--Monitoring.

Water-pipes.

Physical Description:

1 online resource (143 p.)

Edition:

1st ed.

Place of Publication:

London, England ; Hoboken, New Jersey : iSTE : Wiley, 2016.

Summary:

This book presents research work into the reliability of drinking water pipes. The infrastructure of water pipes is susceptible to routine failures, namely leakage or breakage, which occur in an aggregative manner in pipeline networks. Creating strategies for infrastructure asset management requires accurate modeling tools and first-hand experience of what repeated failures can mean in terms of socio-economic and environmental consequences. Devoted to the counting process framework when dealing with this issue, the author presents preliminary basic concepts, particularly the process intensity, as well as basic tools (classical distributions and processes). The introductory material precedes the discussion of several constructs, namely the non-homogeneous birth process, and further as a special case, the linearly extended Yule process (LEYP), and its adaptation to account for selective survival. The practical usefulness of the theoretical results is illustrated with actual water pipe failure data.

Contents:

Cover

Title Page

Copyright

Contents

Preface

Chapter 1: Introduction

1.1. Notation

1.2. General theoretical framework

1.2.1. The concept of a counting process

1.2.2. The intensity function of a counting process

1.3. The non-homogeneous Poisson process

1.4. The Eisenbeis model

1.5. Other approaches for water pipe failure modeling

1.6. Why mobilize the Yule process?

1.7. Structure of the book

Chapter 2: Preliminaries

2.1. The Yule process and the negative binomial distribution

2.2. Gamma-mixture of NHPP

2.3. The negative binomial power series

2.4. The negative multinomial distribution

2.5. The negative multinomial power series

Chapter 3: Non-homogeneous Birth Process

3.1. NHBP intensity

3.2. Conditional distribution of the counting process

Chapter 4: Linear Extension of the Yule Process

4.1. LEYP intensity

4.2. Conditional distribution of the LEYP

4.2.1. Distribution of N(b) − N(a) | N(a−)

4.2.2. Marginal distribution of N(t)

4.2.3. Marginal distribution of N(b) − N(a)

4.2.4. Conditional distribution of N(a−) given N(b) − N(a)

4.2.5. Conditional distribution of N(c) − N(b) given N(b−) − N(a)

4.2.6. Distribution of N(b−) − N(a) given N(c) − N(b)

4.2.7. Distribution of N(d) − N(c) given N(b) − N(a)

4.3. Limiting distribution when α tends to 0+

4.4. Partition of an interval

4.5. Generalization to any subset of a partition

4.6. Discontinuous observation interval

Chapter 5: LEYP Likelihood and Inference

5.1. LEYP likelihood

5.2. LEYP parameter estimation

5.2.1. Maximum likelihood estimator

5.2.2. Null hypothesis of parameter estimates

5.2.3. The Yule-Weibull-Cox intensity

5.2.4. Null hypothesis test implemented for the Yule-Weibull-Cox intensity

5.2.5. Parameter estimation algorithm.

5.3. Validation of the estimation procedure

5.3.1. Conditional distribution of the inter-event time

5.3.2. LEYP event simulation

5.4. LEYP model goodness of fit

5.5. Validating LEYP model predictions

5.5.1. Lorenz curve

5.5.2. Prediction bias checking

Chapter 6: Selective Survival

6.1. Left-truncation, right-censoring and decommissioning decisions

6.2. Coupling failure and decommissioning processes: LEYP2s model

6.3. LEYP2s discretization scheme

6.4. Failure and decommissioning probabilities

6.4.1. Probability of no decommissioning

6.4.2. Distribution of N(b) − N(a) given R(a−) = 0

6.4.3. Conditional probability of R(a−) = 0 given N(b) − N(a)

6.4.4. Conditional distribution of N(c) − N(b) given N(b) − N(a) and R(a−) = 0

6.4.5. Conditional distribution of N(d) − N(c) given N(b) − N(a) and R(a−) = 0

6.4.6. Conditional distribution of N(a−) given N(b) − N(a) and R(a−) = 0

Chapter 7: LEYP2s Likelihood and Inference

7.1. Validation of the estimation procedure for LEYP2s

7.1.1. Constrained and selective decommissioning survival functions

7.1.2. Random failure and decommissioning data generation

7.1.3. Checking parameter estimate accuracy

7.1.4. Checking log-likelihood convexity

Chapter 8: Case Study Application of the LEYP2s Model

8.1. Lausanne water utility

8.2. Lausanne water supply network

8.3. Lausanne network segment failure and decommissioning data

8.4. Model parameter estimates

8.5. Model goodness of fit assessment

8.6. Model validation

8.7. Service lifetime

Chapter 9: Conclusion and Outlook

9.1. Software implementation: Casses

9.2. Model enhancement needs

9.2.1. More flexible analytical form for the failure intensity function

9.2.2. Time-dependent covariates

9.3. LEYP2s model as element of IAM decision helping.

9.3.1. Accounting for vulnerability to failures: toward a risk approach

Appendices

Appendix A: Product Integration

Appendix B: An Algebraic Identity

Bibliography

Index.

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (ebrary, viewed February 17, 2016).

ISBN:

9781119261322

1119261325

9781119261308

1119261309

OCLC:

935251718