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Reliability Theory : With Applications to Preventive Maintenance - Ilya Gertsbakh

Reliability Theory

With Applications to Preventive Maintenance

Hardcover Published: 25th April 2005
ISBN: 9783540672753
Number Of Pages: 219

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The material in this book was first presented as a one-semester course in Relia­ bility Theory and Preventive Maintenance for M.Sc. students of the Industrial Engineering Department of Ben Gurion University in the 1997/98 and 1998/99 academic years. Engineering students are mainly interested in the applied part of this theory. The value of preventive maintenance theory lies in the possibility of its imple­ mentation, which crucially depends on how we handle statistical reliability data. The very nature of the object of reliability theory - system lifetime - makes it extremely difficult to collect large amounts of data. The data available are usu­ ally incomplete, e.g. heavily censored. Thus, the desire to make the course material more applicable led me to include in the course topics such as mod­ eling system lifetime distributions (Chaps. 1,2) and the maximum likelihood techniques for lifetime data processing (Chap. 3). A course in the theory of statistics is aprerequisite for these lectures. Stan­ dard courses usually pay very little attention to the techniques needed for our purpose. A short summary of them is given in Chap. 3, including widely used probability plotting. Chapter 4 describes the most useful and popular models of preventive main­ tenance and replacement. Some practical aspects of applying these models are addressed, such as treating uncertainty in the data, the role of data contamina­ tion and the opportunistic scheduling of maintenance activities.

Industry Reviews

From the reviews:


"...a welcome addition to the resources our profession possesses to learn from, teach from, and refer to...Overall, this is a wonderful book. The theory is sound, the examples are practical, real concerns are treated, and the exposition, although economical, is well organized and logically laid out...As a resource for self-study and as a reference for the professional, this book is an example for others to follow."


"This book gives a very concrete introduction to basic preventive maintenance policies in reliability theory. The material is presented in an elementary way which makes it accessible for readers with basic knowledge of calculus, probability and statistics. Each chapter is concluded by a series of problems with detailed solutions. Overall, the book can be used as an excellent master-level textbook in maintenance policy for graduate students in industrial engineering, operation research, applied probability and statistics...The book is quite nicely written...One special feature of this book is that it contains many interesting examples, which are used for illustrating the basic concepts and theory."

Prefacep. vii
System Reliability as a Function of Component Reliabilityp. 1
The System and Its Componentsp. 1
Independent Components: System Reliability and Stationary Availabilityp. 5
Lifetime Distribution of a System without Component Renewalp. 10
Exercisesp. 14
Parametric Lifetime Distributionsp. 17
Poisson Process - Exponential and Gamma Distributionsp. 17
Aging and Failure Ratep. 24
Normal, Lognormal and Weibull Familiesp. 29
Normal and Lognormal Distributionsp. 29
The Weibull distributionp. 32
Exercisesp. 38
Statistical Inference from Incomplete Datap. 41
Kaplan-Meier Estimator of the Reliability Functionp. 41
Probability Paperp. 44
Parameter Estimation for Censored and Grouped Datap. 50
The Maximum Likelihood Methodp. 50
Maximum Likelihood Function for Censored and Grouped Datap. 51
Finding Maximum Likelihood Estimates for a Censored Sample: Weibull and lognormal Distributionp. 54
Point and Confidence Estimation of Location and ScaleParameters Based on Linear Combination of Order Statis-ticsp. 57
Large-Sample Maximum Likelihood Confidence Intervalsp. 62
Exercisesp. 63
Preventive Maintenance Models Based on the Lifetime Distri-butionp. 67
Basic Facts from Renewal Theory and Reward Processesp. 67
Renewal Processp. 67
Renewal Reward Processp. 72
Alternating Renewal Process. Component Stationary Im-portance Measure for a Renewable Systemp. 74
Principal Models of Preventive Maintenancep. 77
Periodic (Block) Replacement - Cost-type Criterionp. 77
Block Replacement: Availability Criterionp. 78
Periodic Group Repair - Operation Time Based Criterionp. 79
Periodic Preventive Maintenance with Minimal Repairp. 81
Age Replacement - Cost-type Criterionp. 84
Age Replacement - Availability-type Criterionp. 85
Qualitative Investigation of Age and Block Preventive Maintenancep. 86
The Principal Behavior of (T)p. 86
Which is Better: Age or Block Replacement?p. 88
Finding the Optimal Maintenance Period (Age) T*p. 88
Contamination of F(t) by Early Failuresp. 89
Treating Uncertainty in Datap. 89
Age Replacement for the IFR Familyp. 91
Age Replacement with Cost Discountingp. 92
Random Choice of Preventive Maintenance Periodsp. 94
Optimal Opportunistic Preventive Maintenance of a Multiele-ment Systemp. 96
Introductionp. 96
System Description - Coordination of Maintenance Ac-tions - Cost Structurep. 97
Optimization Algorithm. Basic Sequencep. 99
Discussion - Possible Generalizationsp. 101
Exercisesp. 102
Preventive Maintenance Based on Parameter Controlp. 107
Introduction - System Parameter Controlp. 107
Optimal Maintenance of a Multiline Systemp. 109
Preventive Maintenance in a Two-Stage Failure Modelp. 111
The Failure Modelp. 111
Preventive Maintenance. Costsp. 112
Some Facts about the Nonhomogeneous Poisson Processp. 112
Finding the Optimal Location of the PM Pointsp. 114
Markov-Type Processes with Rewards (Costs)p. 116
Markov Chainp. 116
Semi-Markov Processp. 117
SMP with Rewards (Costs)p. 119
Continuous-Time Markov Processp. 120
Opportunistic Replacement of a Two-Component Systemp. 122
General Descriptionp. 122
Formal Setting of the Problemp. 123
Numerical Examplep. 124
Discovering a Malfunction in an Automatic Machinep. 127
Problem Descriptionp. 127
Problem Formalizationp. 127
Numerical Examplep. 129
Preventive Maintenance of Objects with Multidimensional State Descriptionp. 130
General Descriptionp. 130
The Best Scalarizationp. 132
Preventive maintenance: multidimensional state descriptionp. 135
Best Time Scale for Age Replacementp. 139
Introductionp. 139
Finding the Optimal Time Scalep. 141
Optimal Time Scale for Age Replacement: Fatigue Datap. 142
Algorithm for Finding the Optimal <$>{cal T}_a<$>p. 145
Complete Samplesp. 145
Right-Censored Samplesp. 146
Quantal-Type Data: Parametric Approachp. 146
Optimal Age Replacement for Fatigue Test Datap. 147
Preventive Maintenance with Learningp. 151
Information Update: Learning from New Datap. 151
Maintenance-Inspection Model with No Information Updatep. 154
Rolling Horizon and Information Updatep. 155
Actual and "Ideal" Rewardsp. 156
Numerical Examplep. 156
Exercises to Chapters 5-7p. 158
Solutions to Exercisesp. 161
Nonhomogeneous Poisson Processp. 187
Definition and Basic Propertiesp. 187
Parametric estimation of the intensity functionp. 190
Covariances and Means of Order Statisticsp. 195
The Laplace Transformp. 199
Probability Paperp. 201
Renewal Functionp. 205
Referencesp. 207
Glossary of Notationp. 213
Indexp. 215
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9783540672753
ISBN-10: 3540672753
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 219
Published: 25th April 2005
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.39 x 15.6  x 1.42
Weight (kg): 0.51
Edition Number: 2
Edition Type: Revised

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