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Modeling Remaining Useful Life Dynamics in Reliability Engineering

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This book applies traditional reliability engineering methods to prognostics and health management (PHM), looking at remaining useful life (RUL) and its dynamics, to enable engineers to effectively and accurately predict machinery and systems useful lifespan. One of the key tools used in defining and implementing predictive maintenance policies is the RUL indicator. However, it is essential to account for the uncertainty inherent to the RUL, as otherwise predictive maintenance strategies can be incorrect. This can cause high costs or, alternatively, inappropriate decisions. Methods used to estimate RUL are numerous and diverse and, broadly speaking, fall into three categories: model-based, data-driven, or hybrid, which uses both. The author starts by building on established theory and looks at traditional reliability engineering methods through their relation to PHM requirements and presents the concept of RUL loss rate. Following on from this, the author presents an innovative general method for defining a nonlinear transformation enabling the mean residual life to become a linear function of time. He applies this method to frequently encountered time-to-failure distributions, such as Weibull and gamma, and degradation processes. Latest research results, including the author’s (some of which are previously unpublished), are drawn upon and combined with very classical work. Statistical estimation techniques are then presented to estimate RUL from field data, and risk-based methods for maintenance optimization are described, including the use of RUL dynamics for predictive maintenance.

The book ends with suggestions for future research, including links with machine learning and deep learning.

The theory is illustrated by industrial examples. Each chapter is followed by a series of exercises.

FEATURES

    • Provides both practical and theoretical background of RUL

    • Describes how the uncertainty of RUL can be related to RUL loss rate

    • Provides new insights into time-to-failure distributions

    • Offers tools for predictive maintenance

    This book will be of interest to engineers, researchers and students in reliability engineering, prognostics and health management, and maintenance management.

    Author(s): Pierre Dersin
    Publisher: CRC Press
    Year: 2023

    Language: English
    Pages: 198
    City: Boca Raton

    Cover
    Half Title
    Title Page
    Copyright Page
    Dedication
    Table of Contents
    Preface
    Acknowledgments
    Author
    1 Introduction
    Bibliography
    2 Reminder of Reliability Engineering Fundamentals
    2.1 Reliability, Failure Rate, RUL, MRL, and RUL Loss Rate
    2.1.1 Reliability, Failure, and Failure Rate
    2.1.2 RUL, MRL, MTTF, and RUL Loss Rate
    2.2 Fundamental Relation Between MRL, Reliability Function and Failure Rate
    2.3 Confidence Interval for RUL. Illustrations On Special Cases
    2.4 Exercises
    Bibliography
    3 The RUL Loss Rate for a Special Class of Time-To-Failure Distributions*: MRL Linear Function of Time
    3.1 Characterizing the Special Family of Distributions
    3.2 Limiting Cases
    3.2.1 Exponential Distribution
    3.2.2 Dirac Distribution
    3.2.3 Uniform Distribution
    3.3 Synopsis
    3.4 RUL Distribution, Coefficient of Variation of TTF and RUL
    3.4.1 Coefficient of Variation of the Time to Failure
    3.4.2 Coefficient of Variation of the RUL
    3.5 Confidence Interval for RUL and Relation to RUL Loss Rate
    3.6 Higher-Order Moments and Moment-Generating Function
    3.6.1 Moment-Generating Function
    3.6.2 Moment-Generating Function for Special TTF Family
    3.7 Cumulative Hazard Function
    3.8 Exercises
    Bibliography
    4 Generalization to an MRL Piecewise-Linear Function of Time
    4.1 Reliability Function, MRL, and Failure Rate
    4.2 Exercises
    Bibliography
    5 Generalization to a Wide Class of Lifetime Distributions
    5.1 Introduction: Generalization Method
    5.2 Nonlinear Time Transformation
    5.3 Confidence Interval for RUL
    5.4 Application to Weibull Distribution
    5.4.1 Derivation of the Nonlinear Transformation
    5.4.2 Derivation of Confidence Intervals for the RUL
    5.5 Application to Gamma Distribution
    5.6 Application to the Lognormal Distribution
    5.7 Application to the Pareto Distribution
    5.8 Application to Continuous Degradation Processes
    5.8.1 Problem Statement
    5.8.2 RUL for Wiener Process With Drift
    5.8.3 RUL for Gamma Process
    5.9 Exercises
    Bibliography
    6 Properties of the Dg Metric
    6.1 Introduction
    6.2 Derivative of G(t)
    6.3 Differential Equation for MRL
    6.3.1 Example: The Rayleigh Distribution
    6.3.2 Other Example: The Gamma Distribution
    6.4 Second Derivative of G(t)
    6.4.1 Weibull Distribution
    6.4.2 Gamma Distribution
    6.5 Upper Bound for the Average RUL Loss Rate
    6.6 Exercises
    Bibliography
    7 Multiple Failure Or Degradation Modes
    7.1 Introduction
    7.2 General Formulation
    7.3 Illustration in Special Case
    7.4 Exercises
    Bibliography
    8 Statistical Estimation Aspects
    8.1 Introduction
    8.2 Nonparametric Estimation
    8.3 Parametric Estimation—Illustration On Two Case Studies
    8.3.1 Parametric Estimation: The Maximum Likelihood Estimation Method
    8.3.1.1 Maximum Likelihood Estimator
    8.3.1.2 Desirable Properties of the Maximum Likelihood Estimator
    8.3.1.3 Derivation of a Confidence Interval
    8.3.2 First Case Study: Light-Emitting Diodes (LEDs)
    8.3.3 Second Case Study: Redundant System
    8.4 Surrogate Model for the G(t) Transformation
    8.5 Bayesian Estimation
    8.6 Exercises
    Bibliography
    9 Implications for Maintenance Optimization
    9.1 Introduction
    9.2 Maintenance Decisions: Balancing Costs and Risks
    9.3 Quantifying Costs and Risks
    9.3.1 Rejuvenation and Maintenance Efficiency
    9.3.2 Minimal Maintenance (ABAO)
    9.3.3 Perfect Maintenance (AGAN)
    9.4 Predictive Maintenance
    9.5 Exercises
    Bibliography
    10 Advanced Topics and Further Research
    10.1 The Gini Index
    10.2 Entropy and the K Parameter
    10.2.1 Entropy
    10.2.2 Differential Entropy
    10.2.2.1 Differential Entropy as a Function of K and . Parameters
    10.3 Perspectives for Future Research
    10.3.1 Complex Systems
    10.3.2 Dynamic Maintenance Policy
    10.3.3 Signal Processing
    10.3.4 Physics and Machine Learning
    Bibliography
    Index