Reliability modeling: (modeling in the fields of dependability, availability, maintainability, and safety engineering)
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Hagen
LiLoLe-Verl.
2001
|
| Series: | Serving life-long learning
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hergestellt on demand. - Erscheint: September 2001 |
| Physical Description: | 366 S. graph. Darst. |
| ISBN: | 393444704X |
Staff View
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Record in the Search Index
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| adam_text | Titel: Reliability modeling
Autor: Schneeweiss, Winfrid G
Jahr: 2001
Table of contents
page
Preface 5
Table of contents 8
0 Introduction 12
0.1 Basic symbols and terms 12
0.2 Basic concepts 16
0.3 Exercises 29
Part I:
Reliability modeling according to
the number of system components 30
1 The single unit (component) 31
1.1 A unit with periodic preventive renewals 35
1.2 A unit with periodic checks 40
1.3 The repairable unit 48
1.3.1 The general case of a repairable unit 48
1.3.2 The Markov case of a repairable unit 51
1.4 Special Missions 53
1.4.1 Intermittent deterministic demands 53
1.4.2 Sporadic demands of short duration 56
1.5 Exercises 60
2 Systems with 2 components 62
2.1 Non-redundant 2-components systems 65
2.2 The simplest case of redundancy 68
2.3 Markov modeling of 2-components systems 79
2.3.1 Stationary solution of Markov model
of 2-components systems 80
2.3.2 Non-stationary solutions of Markov models
of 2-components systems 81
8
2.3.3. Markov mode] of a fallible switch 87
2.4 Exercises 89
3 Systems with 3 components 92
3.1 2-out-of-3 systems 96
3.2 l-out-of-3;G systems 102
3.3 Markov model of 3-componcnts systems 106
3.4 Exercises 109
4 Systems with 4 components Ill
4.1 3-out-of-4:G systems 113
4.2 2-out-of-4:G systems 116
4.3 l-out-of-4:G systems 118
4.4 Four-components systems allowing for
modular decomposition 120
4.5 Reliability modeling philosophy at the borderline
of hand calculations 123
4.6 Exercises 128
5 Selected systems with 5 or a few more components 130
5.1 Single-bridge systems 130
5.2 Double-bridge systems 138
5.3 Small consecutive-k-out-of-n:F systems 141
5.4 Modeling masive standby 144
5.5 Exercises 146
6 System with many components I
(general problems approximations) .147
6.1 Large series/parallel systems 151
6.2 Large m-out-of-n:G systems 157
6.3 Systems with helping neighbors 162
6.3.1 Linear open-ended arrays of components 162
6.3.2 Circular closed arrays of components 165
6.4 Execises 168
7 Systems with many components II
(connectivity problems in graphs) 170
9
7.1 Source-target problem for acyclic digraphs 170
7.2 Source-target problem for graphs 173
7.3 K-terminal problems 173
7.4 Connectivity with constraints 178
7.4.1 Connectivity with a path length
or path delay limit 178
7.4.2 Connectivity with a minimal flow rate demand 180
7.5 Exercises 183
8 More involved reliability modeling aspects I
(aspects concerning a single component) 186
8.1 More on up-times and down-times 186
8.1.1 On steady state availability in the general case 186
8.1.2 Cumulative up-/down-time 189
8.2 Random interferences beyond failures 191
8.2.1 Random renewals of a unit 191
8.2.2 Random checks of a unit 194
8.3 Time redundancy 199
8.3.1 Distribution of the time needed
for a non-interruptible task 199
8.3.2 Distribution of the number of disturbances
prior to task completion 204
8.4 Exercises 206
9 More involved reliability modeling aspects II
(concerning more than one component) 207
9.1 Time to first failure of a duplex system
with repair and cold standby 207
9.2 Modeling repairable systems as queueing systems 212
9.3 Modeling maintenance priorities via Petri nets 216
9.4 Redundancy due to algebraic coding 218
9.5 Software redundancy 223
9.6 Exercises 225
10 Closing remarks 226
11 Solutions of the exercises 231
10
Part II (Appendix):
Mathematical foundations of
reliability/dependability modeling 277
12 Appendix 1: Basic vocabulary of graph theory 278
13 Appendix 2: Basic Boolean functions theory 284
13.1 Boolean indicator variables and all their
functions of one and two variables 284
13.2 Axioms and elementary laws of Boolean algebra 288
13.3 Boolean functions without Boolean operators 291
13.4 Modularization of Boolean functions 303
14 Appendix 3: Basic probability calculus 307
14.1 Boolean algebra of sets 307
14.2 Elementary probability calculus 309
14.3 Random variables 313
15 Appendix 4: Basic Laplace transform theory 320
16 Appendix 5: Basic Markov process theory 325
16.1 Probabilities of states 326
16.2 Duration of states 329
17 Appendix 6: Basic renewal theory 337
18 Appendix 7: Basic theory of Boolean functions
of binary random processes 343
18.1 Expected value of a Boolean function 343
18.2 Mean duration of the value 1 of a Boolean function 346
References 352
Index 361
11
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:53:46Z |
| institution | BVB |
| isbn | 393444704X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009498889 |
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| publishDate | 2001 |
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| publisher | LiLoLe-Verl. |
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| series2 | Serving life-long learning |
| spelling | Schneeweiss, Winfrid G. 1934- Verfasser (DE-588)108494497 aut Reliability modeling (modeling in the fields of dependability, availability, maintainability, and safety engineering) Winfrid G. Schneeweiss Hagen LiLoLe-Verl. 2001 366 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Serving life-long learning Hergestellt on demand. - Erscheint: September 2001 Mathematisches Modell Reliability (Engineering) Mathematical models Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Zuverlässigkeit (DE-588)4059245-5 gnd rswk-swf Zuverlässigkeit (DE-588)4059245-5 s Mathematisches Modell (DE-588)4114528-8 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009498889&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Schneeweiss, Winfrid G. 1934- Reliability modeling (modeling in the fields of dependability, availability, maintainability, and safety engineering) Mathematisches Modell Reliability (Engineering) Mathematical models Mathematisches Modell (DE-588)4114528-8 gnd Zuverlässigkeit (DE-588)4059245-5 gnd |
| subject_GND | (DE-588)4114528-8 (DE-588)4059245-5 |
| title | Reliability modeling (modeling in the fields of dependability, availability, maintainability, and safety engineering) |
| title_auth | Reliability modeling (modeling in the fields of dependability, availability, maintainability, and safety engineering) |
| title_exact_search | Reliability modeling (modeling in the fields of dependability, availability, maintainability, and safety engineering) |
| title_full | Reliability modeling (modeling in the fields of dependability, availability, maintainability, and safety engineering) Winfrid G. Schneeweiss |
| title_fullStr | Reliability modeling (modeling in the fields of dependability, availability, maintainability, and safety engineering) Winfrid G. Schneeweiss |
| title_full_unstemmed | Reliability modeling (modeling in the fields of dependability, availability, maintainability, and safety engineering) Winfrid G. Schneeweiss |
| title_short | Reliability modeling |
| title_sort | reliability modeling modeling in the fields of dependability availability maintainability and safety engineering |
| title_sub | (modeling in the fields of dependability, availability, maintainability, and safety engineering) |
| topic | Mathematisches Modell Reliability (Engineering) Mathematical models Mathematisches Modell (DE-588)4114528-8 gnd Zuverlässigkeit (DE-588)4059245-5 gnd |
| topic_facet | Mathematisches Modell Reliability (Engineering) Mathematical models Zuverlässigkeit |
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