Reliability theory: with applications to preventive maintenance
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2000
|
| Series: | Engineering online library
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 219 S. graph. Darst. |
| ISBN: | 3540672753 |
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| 245 | 1 | 0 | |a Reliability theory |b with applications to preventive maintenance |c Ilya Gertsbakh |
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Record in the Search Index
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| adam_text | Contents
Preface vii
1 System Reliability as a Function of Component Reliability 1
1.1 The System and Its Components 1
1.2 Independent Components: System
Reliability and Stationary Availability 5
1.3 Lifetime Distribution of a System without Component Renewal . 10
1.4 Exercises 14
2 Parametric Lifetime Distributions 17
2.1 Poisson Process Exponential and Gamma Distributions .... 17
2.2 Aging and Failure Rate 24
2.3 Normal, Lognormal and Weibull Families 29
2.3.1 Normal and Lognormal Distributions 29
2.3.2 The Weibull distribution 32
2.4 Exercises 38
3 Statistical Inference from Incomplete Data 41
3.1 Kaplan Meier Estimator of the Reliability Function 41
3.2 Probability Paper 44
3.3 Parameter Estimation for Censored and Grouped Data 50
3.3.1 The Maximum Likelihood Method 50
3.3.2 Maximum Likelihood Function for Censored and
Grouped Data 51
3.3.3 Finding Maximum Likelihood Estimates for a Censored
Sample: Weibull and lognormal Distribution 54
3.3.4 Point and Confidence Estimation of Location and Scale
Parameters Based on Linear Combination of Order Statis
tics 57
3.3.5 Large Sample Maximum Likelihood Confidence
Intervals 62
3.4 Exercises 63
x CONTENTS
4 Preventive Maintenance Models Based on the Lifetime Distri¬
bution 67
4.1 Basic Facts from Renewal Theory and Reward Processes 67
4.1.1 Renewal Process 67
4.1.2 Renewal Reward Process 72
4.1.3 Alternating Renewal Process. Component Stationary Im¬
portance Measure for a Renewable System 74
4.2 Principal Models of Preventive Maintenance 77
4.2.1 Periodic (Block) Replacement Cost type Criterion ... 77
4.2.2 Block Replacement: Availability Criterion 78
4.2.3 Periodic Group Repair Operation Time Based Criterion 79
4.2.4 Periodic Preventive Maintenance with Minimal Repair . 81
4.2.5 Age Replacement Cost type Criterion 84
4.2.6 Age Replacement Availability type Criterion 85
4.3 Qualitative Investigation of Age and Block Preventive Maintenance 86
4.3.1 The Principal Behavior of t)(T) 86
4.3.2 Which is Better: Age or Block Replacement? 88
4.3.3 Finding the Optimal Maintenance Period (Age) T* . . . . 88
4.3.4 Contamination of F(t) by Early Failures 89
4.3.5 Treating Uncertainty in Data 89
4.3.6 Age Replacement for the IFR Family 91
4.3.7 Age Replacement with Cost Discounting 92
4.3.8 Random Choice of Preventive Maintenance Periods .... 94
4.4 Optimal Opportunistic Preventive Maintenance of a Multiele¬
ment System 96
4.4.1 Introduction 96
4.4.2 System Description Coordination of Maintenance Ac¬
tions Cost Structure 97
4.4.3 Optimization Algorithm. Basic Sequence 99
4.4.4 Discussion Possible Generalizations 101
4.5 Exercises 102
5 Preventive Maintenance Based on Parameter Control 107
5.1 Introduction System Parameter Control 107
5.2 Optimal Maintenance of a Multiline System 109
5.3 Preventive Maintenance in a Two Stage Failure Model Ill
5.3.1 The Failure Model Ill
5.3.2 Preventive Maintenance. Costs 112
5.3.3 Some Facts about the Nonhomogeneous Poisson Process . 112
5.3.4 Finding the Optimal Location of the PM Points 114
5.4 Markov Type Processes with Rewards (Costs) 116
5.4.1 Markov Chain 116
5.4.2 Semi Markov Process 117
5.4.3 SMP with Rewards (Costs) 119
5.4.4 Continuous Time Markov Process 120
CONTENTS xi
5.5 Opportunistic Replacement of a Two Component System .... 122
5.5.1 General Description 122
5.5.2 Formal Setting of the Problem 123
5.5.3 Numerical Example 124
5.6 Discovering a Malfunction in an Automatic Machine 127
5.6.1 Problem Description 127
5.6.2 Problem Formalization 127
5.6.3 Numerical Example 129
5.7 Preventive Maintenance of Objects with Multidimensional State
Description 130
5.7.1 General Description 130
5.7.2 The Best Scalarization 132
5.7.3 Preventive maintenance: multidimensional state description 135
6 Best Time Scale for Age Replacement 139
6.1 Introduction 139
6.2 Finding the Optimal Time Scale 141
6.3 Optimal Time Scale for Age Replacement: Fatigue Data 142
6.4 Algorithm for Finding the Optimal Ta 145
6.4.1 Complete Samples 145
6.4.2 Right Censored Samples 146
6.4.3 Quantal Type Data: Parametric Approach 146
6.5 Optimal Age Replacement for Fatigue Test Data 147
7 Preventive Maintenance with Learning 151
7.1 Information Update: Learning from New Data 151
7.2 Maintenance Inspection Model with No Information Update . . 154
7.3 Rolling Horizon and Information Update 155
7.4 Actual and Ideal Rewards 156
7.5 Numerical Example 156
7.6 Exercises to Chapters 5 7 158
Solutions to Exercises 161
Appendix A: Nonhomogeneous Poisson Process 187
A.I Definition and Basic Properties 187
A.2 Parametric estimation of the intensity function 190
Appendix B: Covariances and Means of Order Statistics 195
Appendix C: The Laplace Transform 199
Appendix D: Probability Paper 201
Appendix E: Renewal Function 205
1
xii CONTENTS
References 207
Glossary of Notation 213
Index 215
|
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| id | DE-604.BV013308865 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:43:32Z |
| institution | BVB |
| isbn | 3540672753 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009074441 |
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| physical | XII, 219 S. graph. Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Springer |
| record_format | marc |
| series2 | Engineering online library |
| spelling | Gercbach, Ilʹja B. 1933- Verfasser (DE-588)122234553 aut Reliability theory with applications to preventive maintenance Ilya Gertsbakh Berlin [u.a.] Springer 2000 XII, 219 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Engineering online library Zuverlässigkeitstheorie (DE-588)4195525-0 gnd rswk-swf Zuverlässigkeitstheorie (DE-588)4195525-0 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009074441&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gercbach, Ilʹja B. 1933- Reliability theory with applications to preventive maintenance Zuverlässigkeitstheorie (DE-588)4195525-0 gnd |
| subject_GND | (DE-588)4195525-0 |
| title | Reliability theory with applications to preventive maintenance |
| title_auth | Reliability theory with applications to preventive maintenance |
| title_exact_search | Reliability theory with applications to preventive maintenance |
| title_full | Reliability theory with applications to preventive maintenance Ilya Gertsbakh |
| title_fullStr | Reliability theory with applications to preventive maintenance Ilya Gertsbakh |
| title_full_unstemmed | Reliability theory with applications to preventive maintenance Ilya Gertsbakh |
| title_short | Reliability theory |
| title_sort | reliability theory with applications to preventive maintenance |
| title_sub | with applications to preventive maintenance |
| topic | Zuverlässigkeitstheorie (DE-588)4195525-0 gnd |
| topic_facet | Zuverlässigkeitstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009074441&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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