Recurrent Event Modeling Based on the Yule Process

Application to Water Network Asset Management

Häftad, Engelska, 2015

AvYves Le Gat,France) Le Gat, Yves (National Research Institute of Science and Technology for Environment and Agriculture (IRSTEA)

2 239 kr

Beställningsvara. Skickas inom 7-10 vardagar. Fri frakt för medlemmar vid köp för minst 249 kr.

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.

Produktinformation

Utgivningsdatum2015-12-11
Mått158 x 234 x 8 mm
Vikt218 g
FormatHäftad
SpråkEngelska
Antal sidor144
FörlagISTE Ltd and John Wiley & Sons Inc
ISBN9781848218918

Tillhör följande kategorier

Matematik inom Naturvetenskap och teknik

Preface ixChapter 1. Introduction 11.1. Notation 21.2. General theoretical framework 41.2.1. The concept of a counting process 41.2.2. The intensity function of a counting process 51.3. The non-homogeneous Poisson process 61.4. The Eisenbeis model 71.5. Other approaches for water pipe failure modeling 81.6. Why mobilize the Yule process? 91.7. Structure of the book 10Chapter 2. Preliminaries 132.1. The Yule process and the negative binomial distribution 132.2. Gamma-mixture of NHPP 172.3. The negative binomial power series 192.4. The negative multinomial distribution 192.5. The negative multinomial power series 22Chapter 3. Non-homogeneous Birth Process 233.1. NHBP intensity 243.2. Conditional distribution of the counting process 24Chapter 4. Linear Extension of the Yule Process 334.1. LEYP intensity 334.2. Conditional distribution of the LEYP 344.2.1. Distribution of N(b) − N(a) | N(a−) 344.2.2. Marginal distribution of N(t) 364.2.3. Marginal distribution of N(b) − N(a) 364.2.4. Conditional distribution of N(a−) given N(b) − N(a) 374.2.5. Conditional distribution of N(c) − N(b) given N(b−) − N(a) 384.2.6. Distribution of N(b−) − N(a) given N(c) − N(b) 394.2.7. Distribution of N(d) − N(c) given N(b) − N(a) 404.3. Limiting distribution when α tends to 0+ 424.4. Partition of an interval 444.5. Generalization to any subset of a partition 464.6. Discontinuous observation interval 49Chapter 5. LEYP Likelihood and Inference 515.1. LEYP likelihood 515.2. LEYP parameter estimation 555.2.1. Maximum likelihood estimator 555.2.2. Null hypothesis of parameter estimates 565.2.3. The Yule–Weibull–Cox intensity 565.2.4. Null hypothesis test implemented for the Yule-Weibull-Cox intensity 575.2.5. Parameter estimation algorithm 585.3. Validation of the estimation procedure 585.3.1. Conditional distribution of the inter-event time 595.3.2. LEYP event simulation 595.4. LEYP model goodness of fit 605.5. Validating LEYP model predictions 625.5.1. Lorenz curve 635.5.2. Prediction bias checking 65Chapter 6. Selective Survival 676.1. Left-truncation, right-censoring and decommissioning decisions 676.2. Coupling failure and decommissioning processes: LEYP2s model 686.3. LEYP2s discretization scheme 696.4. Failure and decommissioning probabilities 716.4.1. Probability of no decommissioning 716.4.2. Distribution of N(b) − N(a) given R(a−) = 0 736.4.3. Conditional probability of R(a−) = 0 given N(b) − N(a) 756.4.4. Conditional distribution of N(c) − N(b) given N(b) − N(a) and R(a−) = 0 776.4.5. Conditional distribution of N(d) − N(c) given N(b) − N(a) and R(a−) = 0 786.4.6. Conditional distribution of N(a−) given N(b) − N(a) and R(a−) = 0 79Chapter 7. LEYP2s Likelihood and Inference 837.1. Validation of the estimation procedure for LEYP2s 887.1.1. Constrained and selective decommissioning survival functions 887.1.2. Random failure and decommissioning data generation 897.1.3. Checking parameter estimate accuracy 937.1.4. Checking log-likelihood convexity 94Chapter 8. Case Study Application of the LEYP2s Model 978.1. Lausanne water utility 978.2. Lausanne water supply network 978.3. Lausanne network segment failure and decommissioning data 998.4. Model parameter estimates 1008.5. Model goodness of fit assessment 1048.6. Model validation 1058.7. Service lifetime 108Chapter 9. Conclusion and Outlook 1119.1. Software implementation: Casses 1119.2. Model enhancement needs 1129.2.1. More flexible analytical form for the failure intensity function 1129.2.2. Time-dependent covariates 1129.3. LEYP2s model as element of IAM decision helping 1149.3.1. Accounting for vulnerability to failures: toward a risk approach 115Appendices 117Appendix A 119Appendix B 121Bibliography 123Index 127