| Description |
xiii, 230 pages : illustrations ; 25 cm |
| Series |
Springer series in reliability engineering, 1614-7839 |
|
Springer series in reliability engineering. 1614-7839
|
| Contents |
Contents note continued: 2.3.4.Smooth Estimation in the ARP -- 2.3.5.Smooth Estimation of the Availability Function -- 2.3.6.Consistency of the Bootstrap Approximation of the Availability Function -- 2.3.7.Bootstrap Estimate of the k-Fold Convolution of a Distribution Function -- References -- 3.Models for Minimal Repair -- 3.1.Introduction -- 3.1.1.The Concept of Minimal Repair -- 3.1.2.Basic Concepts for Counting Processes -- 3.1.3.The Model: Non-Homogeneous Poisson Process (NHPP) -- 3.2.Nonparametric Estimation of the Rate of Occurrence of Failures (Rocof) -- 3.2.1.Smooth Estimation of the Rocof -- 3.2.2.Bandwidth Selection: Least-Squares Cross-Validation -- 3.2.3.Bootstrap Confidence Bounds for Rocof -- 3.3.Recurrence Data: The Multiple Realization Setup -- 3.3.1.Estimation Procedures with Observed Failure Times -- 3.3.2.Estimation Procedures with Aggregated Data -- 3.4.Nonparametric Maximum-Likelihood Estimation of the Rocof Under Monotonicity Constraints -- |
|
Contents note continued: 3.4.1.One Realization Setup -- 3.4.2.Multiple Realization Setup -- References -- 4.Models for Imperfect Repair -- 4.1.Introduction -- 4.1.1.Models for Imperfect Repair Based on Conditional Intensities -- 4.1.2.Models for Imperfect Repair Based on Effective Ages -- 4.2.The Trend-Renewal Process -- 4.2.1.Nonparametric Estimation of the Trend Function of a TRP -- 4.2.2.Nonparametric Estimation of the Trend Function Under Monotonicity Constraints -- 4.2.3.Bootstrap Methods for TRPs -- 4.3.Models Based on Effective Ages -- 4.3.1.Nonparametric Statistical Inference for the Brown-Proschan Model -- 4.3.2.Nonparametric Statistical Inference for the Pena-Hollander Model -- 4.3.3.A General Model for Imperfect Repair Based on Effective Ages -- References -- pt. III White-Box Approach: The Physical Environment -- 5.Systems with Multi-Components -- 5.1.From Binary to Continuous-State Reliability Systems -- 5.1.1.Introduction -- 5.1.2.The Structure Function -- |
|
Contents note continued: 5.2.Monotone Regression Analysis of the Structure Function -- 5.2.1.Nonparametric Kernel Regression of the Structure Function -- 5.2.2.The Problem of the Boundary Effect -- 5.2.3.Data-Driven Bandwidth Selection Methods -- 5.2.4.Estimation Under Monotonicity Constraints: Isotonization Procedure -- 5.2.5.Examples -- 5.3.Estimation of Some Performance Measures -- 5.3.1.The Expected State of the System -- 5.3.2.The Probability of Occurrence of Failures -- References -- 6.Reliability of Semi-Markov Systems -- 6.1.Introduction -- 6.2.Markov Renewal and Semi-Markov Processes -- 6.2.1.Definitions -- 6.2.2.Markov Renewal Theory -- 6.2.3.Nonparametric Estimation -- 6.3.Reliability of Semi-Markov Systems -- 6.3.1.Reliability Modeling -- 6.3.2.Reliability Estimation -- 6.4.Reliability in Discrete Time -- 6.4.1.Semi-Markov Chains -- 6.4.2.Reliability Modeling -- 6.5.General State Space Semi-Markov Systems -- 6.5.1.Introduction -- 6.5.2.Reliability Modeling -- |
|
Contents note continued: 6.6.Stationary Probability Estimation and Availability -- 6.6.1.Introduction -- 6.6.2.Weak Invariance Principle -- 6.6.3.Strong Invariance Principle -- References -- 7.Hazard Regression Analysis -- 7.1.Introduction: A Review of Regression Models for Lifetime Data -- 7.1.1.The Cox Proportional Hazards Model -- 7.1.2.The Aalen Additive Model -- 7.1.3.The Accelerated Failure Time Model -- 7.1.4.More General Models -- 7.2.Extending the Cox Proportional Hazards Model -- 7.2.1.Smoothed Estimate of the Baseline Hazard -- 7.2.2.The Generalized Additive Proportional Hazards Model -- 7.3.Nonparametric Hazard Regression -- 7.3.1.Local Linear Smoothing of the Hazard Rate -- References |
|
Machine generated contents note: pt. I Black-Box Approach: Time-to-Failure Analysis -- 1.Lifetime Data -- 1.1.Smoothing Methods for Lifetime Data -- 1.1.1.Introduction -- 1.2.Complete Samples -- 1.3.Censored Samples -- 1.4.Density Estimation with Censored Data -- 1.5.Failure Rate Estimation -- 1.5.1.Local Linear Estimation of the Failure Rate -- 1.5.2.Spline Estimation of the Failure Rate -- 1.6.Asymmetric Kernels -- 1.7.Bandwidth Selection -- 1.7.1.Bayesian Bandwidths -- References -- pt. II Grey-Box Approach: Counting Processes -- 2.Models for Perfect Repair -- 2.1.Introduction -- 2.2.Ordinary Renewal Process -- 2.2.1.The Renewal Function -- 2.2.2.Nonparametric Estimation of the k-Fold Convolution of Distribution Functions -- 2.3.Alternating Renewal Process -- 2.3.1.Introduction and Some Applications of the ARP in Reliability -- 2.3.2.Availability Measures of a Repairable System -- 2.3.3.Nonparametric Estimation of Steady-State Availability -- |
| Summary |
Nonparametric statistics has probably become the leading methodology for researchers performing data analysis. It is nevertheless true that, whereas these methods have already proved highly effective in other applied areas of knowledge such as biostatistics or social sciences, nonparametric analyses in reliability currently form an interesting area of study that has not yet been fully explored. Applied Nonparametric Statistics in Reliability is focused on the use of modern statistical methods for the estimation of dependability measures of reliability systems that operate under different conditions. The scope of the book includes: smooth estimation of the reliability function and hazard rate of non-repairable systems; study of stochastic processes for modelling the time evolution of systems when imperfect repairs are performed; nonparametric analysis of discrete and continuous time semi-Markov processes; isotonic regression analysis of the structure function of a reliability system, and lifetime regression analysis. Besides the explanation of the mathematical background, several numerical computations or simulations are presented as illustrative examples. The corresponding computer-based methods have been implemented using R and MATLAB®. A concrete modelling scheme is chosen for each practical situation and, in consequence, a nonparametric inference procedure is conducted. Applied Nonparametric Statistics in Reliability will serve the practical needs of scientists (statisticians and engineers) working on applied reliability subjects |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Print version record |
| Subject |
Nonparametric statistics -- Industrial applications.
|
|
Reliability (Engineering) -- Statistical methods.
|
| Author |
Gámiz, M. Luz.
|
| LC no. |
2011499848 |
| ISBN |
9780857291172 (cased) |
|
(e-ISBN) |
|
