Recurrent Event Modeling Based on the Yule Process - Application to Water Network Asset Management

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.

List of contents

Preface ix
Chapter 1. Introduction  1
1.1. Notation 2
1.2. General theoretical framework  4
1.2.1. The concept of a counting process  4
1.2.2. The intensity function of a counting process  5
1.3. The non-homogeneous Poisson process 6
1.4. The Eisenbeis model  7
1.5. Other approaches for water pipe failure modeling 8
1.6. Why mobilize the Yule process? 9
1.7. Structure of the book 10
Chapter 2. Preliminaries  13
2.1. The Yule process and the negative binomial distribution  13
2.2. Gamma-mixture of NHPP 17
2.3. The negative binomial power series 19
2.4. The negative multinomial distribution  19
2.5. The negative multinomial power series 22
Chapter 3. Non-homogeneous Birth Process  23
3.1. NHBP intensity  24
3.2. Conditional distribution of the counting process  24
Chapter 4. Linear Extension of the Yule Process  33
4.1. LEYP intensity 33
4.2. Conditional distribution of the LEYP  34
4.2.1. Distribution of N(b) ¿ N(a) | N(ä) 34
4.2.2. Marginal distribution of N(t) 36
4.2.3. Marginal distribution of N(b) ¿ N(a)  36
4.2.4. Conditional distribution of N(ä) given N(b) ¿ N(a) 37
4.2.5. Conditional distribution of N(c) ¿ N(b) given N(b¿) ¿ N(a) 38
4.2.6. Distribution of N(b¿) ¿ N(a) given N(c) ¿ N(b)  39
4.2.7. Distribution of N(d) ¿ N(c) given N(b) ¿ N(a) 40
4.3. Limiting distribution when ¿ tends to 0+  42
4.4. Partition of an interval 44
4.5. Generalization to any subset of a partition  46
4.6. Discontinuous observation interval  49
Chapter 5. LEYP Likelihood and Inference  51
5.1. LEYP likelihood  51
5.2. LEYP parameter estimation  55
5.2.1. Maximum likelihood estimator  55
5.2.2. Null hypothesis of parameter estimates 56
5.2.3. The Yule-Weibull-Cox intensity 56
5.2.4. Null hypothesis test implemented for the Yule-Weibull-Cox intensity 57
5.2.5. Parameter estimation algorithm 58
5.3. Validation of the estimation procedure  58
5.3.1. Conditional distribution of the inter-event time 59
5.3.2. LEYP event simulation  59
5.4. LEYP model goodness of fit 60
5.5. Validating LEYP model predictions 62
5.5.1. Lorenz curve  63
5.5.2. Prediction bias checking 65
Chapter 6. Selective Survival 67
6.1. Left-truncation, right-censoring and decommissioning decisions  67
6.2. Coupling failure and decommissioning processes: LEYP2s model 68
6.3. LEYP2s discretization scheme  69
6.4. Failure and decommissioning probabilities 71
6.4.1. Probability of no decommissioning 71
6.4.2. Distribution of N(b) ¿ N(a) given R(ä) = 0  73
6.4.3. Conditional probability of R(ä) = 0 given N(b) ¿ N(a) 75
6.4.4. Conditional distribution of N(c) ¿ N(b) given N(b) ¿ N(a) and R(ä) = 0 77
6.4.5. Conditional distribution of N(d) ¿ N(c) given N(b) ¿ N(a) and R(ä) = 0 78
6.4.6. Conditional distribution of N(ä) given N(b) ¿ N(a) and R(ä) = 0 79
Chapter 7. LEYP2s Likelihood and Inference  83
7.1. Validation of the estimation procedure for LEYP2s  88
7.1.1. Constrained and selective decommissioning survival functions 88
7.1.2. Random failure and decommissioning data generation  89
7.1.3. Checking parameter estimate accuracy 93
7.1.4. Checking log-likelihood convexity  94
Chapter 8. Case Study Application of the LEYP2s Model  97
8.1. Lausanne water utility 97
8.2. Lausanne water supply network 97
8.3. Lausanne network segment failure and decommissioning data 99
8.4. Model parameter estimates  100
8.5. Model goodness of fit assessment  104
8.6. Model validation  105
8.7. Service lifetime  108
Chapter 9. Conclusion and Outlook  111
9.1. Software implementation: Casses  111
9.2. Model enhancement needs  112
9.2.1. More flexible analytical form for the failure intensity function 112
9.2.2. Time-dependent covariates  112
9.3. LEYP2s model as element of IAM decision helping  114
9.3.1. Accounting for vulnerability to failures: toward a risk approach  115
Appendices  117
Appendix A  119
Appendix B  121
Bibliography 123
Index  127

About the author

Yves Le Gat is a Civil Engineer and Researcher at the National Research Institute of Science and Technology for Environment and Agriculture (IRSTEA), a French governmental institution under the joint supervision of the French ministries in charge of research and agriculture.

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.

Product details

• Authors: Yves Le Gat, Le Gat, Yves Le Gat
• Publisher: Wiley
• Languages: English
• Product format: Paperback / Softback
• Released: 31.01.2016
• EAN: 9781848218918
• ISBN: 978-1-84821-891-8
• No. of pages: 144
• Dimensions: 156 mm x 234 mm x 8 mm
• Weight: 228 g
• Subject: Natural sciences, medicine, IT, technology > Mathematics > Basic principles