Reliability modelling and analysis in discrete time

Reliability modelling and analysis in discrete time

Reliability Modelling and Analysis in Discrete Time provides an overview of the probabilistic and statistical aspects connected with discrete reliability systems. This engaging book discusses their distributional properties and dependence structures before exploring various orderings associated betw...

Descripción completa

Detalles Bibliográficos
Otros Autores: Nair, N. Unnikrishnan, author (author), Sankaran, P. G., author, Balakrishnan, N., author
Formato: Libro electrónico
Idioma:Inglés
Publicado: London : Academic Press [2018]
Edición:First edition
Materias:
Reliability (Engineering) > Mathematical models.
Ver en Biblioteca Universitat Ramon Llull:https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009630712506719
Tabla de Contenidos:
  • Front Cover
  • Reliability Modelling and Analysis in Discrete Time
  • Copyright
  • Dedication
  • Contents
  • Authors Biographies
  • Preface
  • About the Book
  • 1 Reliability Theory
  • 1.1 Reliability Theory
  • 1.2 Discrete Life Distributions
  • 1.3 Mixture Distributions
  • 1.4 Weighted Distributions
  • 1.5 Convolution
  • 1.6 Shock Models
  • 1.7 Convexity and Related Concepts
  • 1.8 Multivariate Distributions
  • 1.9 Multivariate Weighted Distributions
  • 1.10 Dependence Measures and Concepts
  • 1.10.1 Measures of Dependence
  • Kendall's Tau
  • Spearman's Rho
  • Blomqvist's ß
  • 1.10.2 Dependence Concepts
  • 1.10.3 Multivariate Dependence
  • 1.10.4 Time-Dependent Measures
  • 1.11 Schur Convexity and Concavity
  • 2 Basic Reliability Concepts
  • 2.1 Introduction
  • 2.2 Hazard Rate Function
  • 2.3 Mean Residual Life
  • 2.3.1 Modelling Data
  • 2.4 Variance Residual Life Function
  • 2.5 Upper Partial Moments
  • 2.6 Reversed Hazard Rate
  • 2.7 Reversed Mean Residual Life
  • 2.8 Reversed Variance Residual Life
  • 2.9 Odds Function
  • 2.10 Log-odds Functions and Rates
  • 2.11 Mixture Distributions
  • 2.12 Weighted Distributions
  • 3 Discrete Lifetime Models
  • 3.1 Introduction
  • 3.2 Families of Distributions
  • 3.2.1 Ord Family
  • 3.2.2 Power Series Family
  • 3.2.3 Lerch Family
  • Geometric Distribution
  • Discrete Uniform Distribution
  • Discrete Pareto
  • Hurwitz-Zeta Distribution
  • 3.2.4 Abel Series Distributions
  • Generalized Poisson Distribution
  • Quasi-Binomial Distribution I
  • Quasi-Negative Binomial Distribution
  • Quasi-Logarithmic Series Distribution
  • Quasi-Binomial Distribution II
  • 3.2.5 Lagrangian Family
  • Haight Distribution
  • Geeta Distribution
  • Generalized Geometric Distribution II
  • 3.3 Discrete Analogues of Continuous Distributions
  • Discrete Weibull Distribution
  • Discrete Half-Logistic Distribution.
  • Geometric Weibull Distribution
  • Telescopic Distributions
  • Discrete Inverse Weibull Distribution
  • Discrete Generalized Exponential Distribution
  • Discrete Gamma Distribution
  • Discrete Lindley Distribution
  • 3.4 Some Other Models
  • Discrete Weibull Distribution II
  • Discrete Weibull Distribution III
  • S" Distribution
  • 4 Discrete Ageing Concepts
  • 4.1 Introduction
  • 4.2 Stochastic Orders
  • 4.3 Classes Based on Hazard Rate
  • 4.3.1 Monotone Hazard Rates
  • 4.3.2 Increasing Hazard Rate (2)
  • 4.3.3 Increasing Hazard Rate Average
  • 4.3.4 Now Better Than Used in Hazard Rate
  • 4.4 Classes Based on Residual Life
  • 4.4.1 Decreasing Mean Residual Life
  • 4.4.2 Decreasing Mean Residual Life in Harmonic Average
  • 4.4.3 Used Better Than Aged
  • 4.4.4 Decreasing Variance Residual Life
  • 4.5 Classes Based on Survival Function
  • 4.5.1 New Better Than Used
  • 4.5.2 New Better Than Used in Expectation
  • 4.5.3 Harmonically New Better That Used in Expectation
  • 4.6 Classes Based on Reliability Functions in Reversed Time
  • 4.6.1 Decreasing Reversed Hazard Rate
  • 4.6.2 Increasing Mean Inactivity Time
  • 4.6.3 Increasing Variance Inactivity Time
  • 4.7 Ageing Properties for Weighted Distributions
  • 4.8 Relative Ageing
  • 4.8.1 Ordering by Ageing Concepts
  • 4.8.2 Speci c Ageing Factor
  • 4.8.3 Ageing Intensity Function
  • 5 Bathtub Distributions
  • 5.1 Introduction
  • 5.2 De nitions and Techniques for Identi cation of Bathtub Distributions
  • 5.3 Models
  • 5.3.1 Inverse Weibull Model
  • 5.3.2 Competing Risk Models
  • 5.3.3 Modi ed Weibull Distribution
  • 5.3.4 Additive Weibull Distribution
  • 5.3.5 Modi ed Weibull Extension
  • 5.3.6 Discrete Reduced Modi ed Weibull Distribution
  • 5.4 Methods of Constructing Bathtub Models
  • 5.4.1 Discretizing Continuous Distributions
  • 5.4.2 Using General Conditions
  • 5.4.3 Construction From Mixtures.
  • 5.4.4 Convex Functions
  • 5.5 Properties of BT Models
  • 5.6 Other Forms of Non-monotonic Hazard Rates
  • 6 Multivariate Reliability Concepts
  • 6.1 Introduction
  • 6.2 Multivariate Hazard Rate
  • 6.2.1 Scalar Hazard Rate
  • 6.2.2 Conditional Hazard Rate
  • 6.2.3 Vector Hazard Rate
  • 6.2.4 Total Hazard Rate
  • 6.2.5 Alternative Conditional Hazard Rate
  • 6.2.6 Constancy of Hazard Rates
  • 6.3 Multivariate Mean Residual Life
  • 6.3.1 Conditional Mean Residual Life
  • 6.4 Variance Residual Life Functions
  • 6.4.1 Bivariate Variance Residual Life
  • 6.4.2 Covariance Residual Life
  • 6.5 Multivariate Reversed Hazard Rate
  • 6.5.1 Scalar Reversed Hazard Rate
  • 6.5.2 Vector Reversed Hazard Rate
  • 6.5.3 Conditional Reversed Hazard Rate
  • 6.6 Reversed Mean Residual Life Function
  • 6.7 Bivariate Reversed Variance Residual Life
  • 6.8 Reliability Functions and Time Dependent Measures of Association
  • 6.9 Reliability Functions of Equilibrium Distributions
  • Model 1
  • Model 2
  • Model 3
  • 7 Multivariate Ageing Concepts
  • 7.1 Introduction
  • 7.2 Multivariate Stochastic Orders
  • 7.3 Multivariate No-ageing
  • 7.4 Multivariate IHR Classes
  • 7.5 Bayesian Approach to Ageing Classes
  • 7.6 Multivariate Increasing Hazard Rate Average
  • 7.7 New Better Than Used in Hazard Rate
  • 7.8 Multivariate Decreasing Mean Residual Life
  • 7.9 Decreasing Conditional Mean Residual Life
  • 7.10 Bayesian De nition of DMRL Distributions
  • 7.11 Multivariate New Better Than Used Class
  • 7.12 Multivariate New Better Than Used in Expectation
  • 7.13 Multivariate Harmonic New Better Than Used in Expectation
  • 7.14 Increasing Product Moment Residual Life
  • 8 Multivariate Lifetime Models
  • 8.1 Introduction
  • 8.2 Multivariate Geometric Distributions
  • 8.2.1 Geometric Distribution-1
  • 8.2.2 Multivariate Geometric Distribution-2
  • 8.2.3 Multivariate Geometric Distribution-3.
  • 8.2.4 Multivariate Geometric Distribution-4
  • 8.2.5 Bivariate Geometric Distribution-6
  • 8.2.6 Bivariate Geometric Distribution-7
  • 8.3 Schur-Constant Family
  • 8.3.1 Distributional Features
  • 8.3.2 Reliability Aspects
  • 8.3.3 Dependence and Ageing
  • 8.4 Bivariate Waring Distribution-1
  • 8.5 Bivariate Waring Distribution-2
  • 8.6 Bivariate Negative Hypergeometric Distribution
  • 8.7 Bivariate Weibull Distribution
  • 8.8 Multivariate Zipf Distributions
  • 9 Applications
  • 9.1 Introduction
  • 9.2 Survival Analysis
  • 9.2.1 Proportional Hazards Models
  • 9.2.2 Additive Hazards Model
  • 9.2.3 Proportional Reversed Hazards Model
  • 9.2.4 Proportional Mean Residual Life Model
  • 9.2.5 Proportional Odds Model
  • 9.3 Social Sciences
  • 9.4 Risk Analysis
  • 9.5 Information Theory
  • 9.6 Mathematics and Statistics
  • References
  • Index
  • Back Cover.

Ejemplares similares