Recurrent Event Modeling Based on the Yule Process E-Book

Yves Le Gat

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 109

Veröffentlichungsjahr: 2015

Beschreibung

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.

Leseprobe

Table of Contents

Cover

Title

Copyright

Preface

1 Introduction

1.1. Notation

1.2. General theoretical framework

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

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

3 Non-homogeneous Birth Process

3.1. NHBP intensity

3.2. Conditional distribution of the counting process

4 Linear Extension of the Yule Process

4.1. LEYP intensity

4.2. Conditional distribution of the LEYP

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

5 LEYP Likelihood and Inference

5.1. LEYP likelihood

5.2. LEYP parameter estimation

5.3. Validation of the estimation procedure

5.4. LEYP model goodness of fit

5.5. Validating LEYP model predictions

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

7 LEYP2s Likelihood and Inference

7.1. Validation of the estimation procedure for LEYP2s

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