Stochastic models in reliability:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
1999
|
| Series: | Applications of mathematics
41 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 253 - 265 |
| Physical Description: | XII, 270 S. Ill., graph. Darst. |
| ISBN: | 0387986332 |
Staff View
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| 100 | 1 | |a Aven, Terje |d 1956- |e Verfasser |0 (DE-588)120986469 |4 aut | |
| 245 | 1 | 0 | |a Stochastic models in reliability |c Terje Aven ; Uwe Jensen |
| 264 | 1 | |a New York [u.a.] |b Springer |c 1999 | |
| 300 | |a XII, 270 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Applications of mathematics |v 41 | |
| 500 | |a Literaturverz. S. 253 - 265 | ||
| 650 | 4 | |a Zuverlässigkeitstheorie - Stochastischer Prozess | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Reliability (Engineering) -- Mathematical models | |
| 650 | 4 | |a Stochastic processes | |
| 650 | 0 | 7 | |a Zuverlässigkeitstheorie |0 (DE-588)4195525-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Stochastischer Prozess |0 (DE-588)4057630-9 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Jensen, Uwe |d 1958- |e Verfasser |0 (DE-588)122561368 |4 aut | |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-008526144 | |
Record in the Search Index
| _version_ | 1807500891994980352 |
|---|---|
| adam_text |
CONTENTS
1
INTRODUCTION
1
1.1
LIFETIME
MODELS
.
1
1.1.1
COMPLEX
SYSTEMS
.
2
1.1.2
DAMAGE
MODELS
.
3
1.1.3
DIFFERENT
INFORMATION
LEVELS
.
5
1.1.4
SIMPSON
'
S
PARADOX
.
5
1.1.5
PREDICTABLE
LIFETIME
.
5
1.1.6
A
GENERAL
FAILURE
MODEL
.
6
1.2
MAINTENANCE
.
8
1.2.1
AVAILABILITY
ANALYSIS
.
8
1.2.2
OPTIMIZATION
MODELS
.
9
1.3
RELIABILITY
MODELING
.
10
1.3.1
NUCLEAR
POWER
STATION
.
12
1.3.2
GAS
COMPRESSION
SYSTEM
.
14
2
BASIC
RELIABILITY
THEORY
19
2.1
COMPLEX
SYSTEMS
.
19
2.1.1
BINARY
MONOTONE
SYSTEMS
.
19
2.1.2
MULTISTATE
MONOTONE
SYSTEMS
.
33
2.2
BASIC
NOTIONS
OF
AGING
.
37
2.2.1
NONPARAMETRIC
CLASSES
OF
LIFETIME
DISTRIBUTIONS
.
.
38
2.2.2
CLOSURE
THEOREMS
.
41
2.2.3
STOCHASTIC
COMPARISON
.
43
X
CONTENTS
3
STOCHASTIC
FAILURE
MODELS
47
3.1
NOTATION
AND
FUNDAMENTALS
.
47
3.1.1
THE
SEMIMARTINGALE
REPRESENTATION
.
50
3.1.2
TRANSFORMATIONS
OF
SMOOTH
SEMIMARTINGALES
.
59
3.2
A
GENERAL
LIFETIME
MODEL
.
61
3.2.1
EXISTENCE
OF
FAILURE
RATE
PROCESSES
.
63
3.2.2
FAILURE
RATE
PROCESSES
IN
COMPLEX
SYSTEMS
.
65
3.2.3
MONOTONE
FAILURE
RATE
PROCESSES
.
69
3.2.4
CHANGE
OF
INFORMATION
LEVEL
.
70
3.3
POINT
PROCESSES
IN
RELIABILITY
-
FAILURE
TIME
AND
REPAIR
MODELS
.
73
3.3.1
ALTERNATING
RENEWAL
PROCESSES
-
ONE-COMPONENT
SYSTEMS
WITH
REPAIR
.
76
3.3.2
NUMBER
OF
SYSTEM
FAILURES
FOR
MONOTONE
SYSTEMS
.
77
3.3.3
COMPOUND
POINT
PROCESS
-
SHOCK
MODELS
.
79
3.3.4
SHOCK
MODELS
WITH
STATE-DEPENDENT
.
FAILURE
PROBABILITY
.
80
3.3.5
SHOCK
MODELS
WITH
FAILURES
OF
THRESHOLD
TYPE
.
81
3.3.6
MINIMAL
REPAIR
MODELS
.
82
3.3.7
COMPARISON
OF
REPAIR
PROCESSES
FOR
DIFFERENT
.
INFORMATION
LEVELS
.
87
3.3.8
REPAIR
PROCESSES
WITH
VARYING
DEGREES
OF
REPAIR
.
.
90
3.3.9
MINIMAL
REPAIRS
AND
PROBABILITY
OF
RUIN
.
91
4
AVAILABILITY
ANALYSIS
OF
COMPLEX
SYSTEMS
97
4.1
PERFORMANCE
MEASURES
.
98
4.2
ONE-COMPONENT
SYSTEMS
.
99
4.2.1
POINT
AVAILABILITY
.
101
4.2.2
THE
DISTRIBUTION
OF
THE
NUMBER
OF
SYSTEM
FAILURES
.
102
4.2.3
THE
DISTRIBUTION
OF
THE
DOWNTIME
.
IN
A
TIME
INTERVAL
.
108
4.2.4
STEADY-STATE
DISTRIBUTION
.
ILL
4.3
POINT
AVAILABILITY
AND
MEAN
NUMBER
OF
SYSTEM
FAILURES
.
.
112
4.3.1
POINT
AVAILABILITY
.
113
4.3.2
MEAN
NUMBER
OF
SYSTEM
FAILURES
.
113
4.4
DISTRIBUTION
OF
THE
NUMBER
OF
SYSTEM
FAILURES
.
117
4.4.1
ASYMPTOTIC
ANALYSIS
FOR
THE
TIME
TO
THE
FIRST
.
.
.
SYSTEM
FAILURE
.
119
4.4.2
SOME
SUFFICIENT
CONDITIONS
.
123
4.4.3
ASYMPTOTIC
ANALYSIS
OF
THE
NUMBER
.
OF
SYSTEM
FAILURES
.
128
4.5
DOWNTIME
DISTRIBUTION
GIVEN
SYSTEM
FAILURE
.
138
4.5.1
PARALLEL
SYSTEM
.
138
4.5.2
GENERAL
MONOTONE
SYSTEM
.
141
4.5.3
DOWNTIME
DISTRIBUTION
OF
THE
ITH
SYSTEM
FAILURE
.
.
141
CONTENTS
XI
4.6
DISTRIBUTION
OF
THE
SYSTEM
DOWNTIME
IN
AN
INTERVAL
.
144
4.6.1
COMPOUND
POISSON
PROCESS
APPROXIMATION
.
144
4.6.2
ASYMPTOTIC
ANALYSIS
.
146
4.7
GENERALIZATIONS
AND
RELATED
MODELS
.
151
4.7.1
MULTISTATE
MONOTONE
SYSTEMS
.
151
4.7.2
PARALLEL
SYSTEM
WITH
REPAIR
CONSTRAINTS
.
158
4.7.3
STANDBY
SYSTEMS
.
159
5
MAINTENANCE
OPTIMIZATION
169
5.1
BASIC
REPLACEMENT
MODELS
.
169
5.1.1
AGE
REPLACEMENT
POLICY
.
169
5.1.2
BLOCK
REPLACEMENT
POLICY
.
171
5.1.3
COMPARISONS
AND
GENERALIZATIONS
.
172
5.2
A
GENERAL
REPLACEMENT
MODEL
.
175
5.2.1
AN
OPTIMAL
STOPPING
PROBLEM
.
175
5.2.2
A
RELATED
STOPPING
PROBLEM
.
177
5.2.3
DIFFERENT
INFORMATION
LEVELS
.
184
5.3
APPLICATIONS
.
185
5.3.1
THE
GENERALIZED
AGE
REPLACEMENT
MODEL
.
185
5.3.2
A
SHOCK
MODEL
OF
THRESHOLD
TYPE
.
188
5.3.3
INFORMATION-BASED
REPLACEMENT
OF
COMPLEX
SYSTEMS
189
5.3.4
A
PARALLEL
SYSTEM
WITH
TWO
DEPENDENT
COMPONENTS
192
5.3.5
COMPLETE
INFORMATION
ABOUT
71,72
AND
T
.
193
5.3.6
A
BURN-IN
MODEL
.
197
5.4
REPAIR
REPLACEMENT
MODELS
.
202
5.4.1
OPTIMAL
REPLACEMENT
UNDER
.
A
GENERAL
REPAIR
STRATEGY
.
202
5.4.2
A
MARKOV-MODULATED
REPAIR
PROCESS
-
OPTIMIZA
TION
WITH
PARTIAL
INFORMATION
.
203
5.4.3
THE
CASE
OF
M=2
STATES
.
209
A
BACKGROUND
IN
PROBABILITY
AND
STOCHASTIC
PROCESSES
213
A.L
BASIC
DEFINITIONS
.
213
A.
2
RANDOM
VARIABLES,
CONDITIONAL
EXPECTATIONS
.
215
A.
2.1
RANDOM
VARIABLES
AND
EXPECTATIONS
.
215
A.
2.2
L
P
-SPACES
AND
CONDITIONING
.
217
A.
2.3
PROPERTIES
OF
CONDITIONAL
EXPECTATIONS
.
219
A.
2.4
REGULAR
CONDITIONAL
PROBABILITIES
.
221
A.
2.5
COMPUTATION
OF
CONDITIONAL
EXPECTATIONS
.
221
A.
3
STOCHASTIC
PROCESSES
ON
A
FILTERED
PROBABILITY
SPACE
.
223
A.
4
STOPPING
TIMES
.
226
A.
5
MARTINGALE
THEORY
.
229
A.
6
SEMIMARTINGALES
.
235
A.
6.1
CHANGE
OF
TIME
.
237
A.
6.2
PRODUCT
RULE
.
237
XII
CONTENTS
B
RENEWAL
PROCESSES
243
B.L
B.2
B.3
B.4
BASIC
THEORY
OF
RENEWAL
PROCESSES
.
243
RENEWAL
REWARD
PROCESSES
.
250
REGENERATIVE
PROCESSES
.
251
MODIFIED
(DELAYED)
PROCESSES
.
252
REFERENCES
253
INDEX
266 |
| any_adam_object | 1 |
| author | Aven, Terje 1956- Jensen, Uwe 1958- |
| author_GND | (DE-588)120986469 (DE-588)122561368 |
| author_facet | Aven, Terje 1956- Jensen, Uwe 1958- |
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| building | Verbundindex |
| bvnumber | BV012556915 |
| callnumber-first | T - Technology |
| callnumber-label | TA169 |
| callnumber-raw | TA169.A95 1999 |
| callnumber-search | TA169.A95 1999 |
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| callnumber-subject | TA - General and Civil Engineering |
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| classification_tum | DAT 286f MAT 606f |
| ctrlnum | (OCoLC)245818504 (DE-599)BVBBV012556915 |
| dewey-full | 620/.00452/01511821 620/.00452/015118 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 620 - Engineering and allied operations |
| dewey-raw | 620/.00452/015118 21 620/.00452/015118 |
| dewey-search | 620/.00452/015118 21 620/.00452/015118 |
| dewey-sort | 3620 3452 515118 221 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Informatik Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV012556915 |
| illustrated | Illustrated |
| indexdate | 2024-08-16T00:12:57Z |
| institution | BVB |
| isbn | 0387986332 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008526144 |
| oclc_num | 245818504 |
| open_access_boolean | |
| owner | DE-384 DE-945 DE-824 DE-703 DE-20 DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-521 DE-83 DE-11 DE-188 DE-706 |
| owner_facet | DE-384 DE-945 DE-824 DE-703 DE-20 DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-521 DE-83 DE-11 DE-188 DE-706 |
| physical | XII, 270 S. Ill., graph. Darst. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Springer |
| record_format | marc |
| series | Applications of mathematics |
| series2 | Applications of mathematics |
| spelling | Aven, Terje 1956- Verfasser (DE-588)120986469 aut Stochastic models in reliability Terje Aven ; Uwe Jensen New York [u.a.] Springer 1999 XII, 270 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Applications of mathematics 41 Literaturverz. S. 253 - 265 Zuverlässigkeitstheorie - Stochastischer Prozess Mathematisches Modell Reliability (Engineering) -- Mathematical models Stochastic processes Zuverlässigkeitstheorie (DE-588)4195525-0 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Zuverlässigkeitstheorie (DE-588)4195525-0 s Stochastischer Prozess (DE-588)4057630-9 s DE-604 Jensen, Uwe 1958- Verfasser (DE-588)122561368 aut Applications of mathematics 41 (DE-604)BV000895226 41 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008526144&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Aven, Terje 1956- Jensen, Uwe 1958- Stochastic models in reliability Applications of mathematics Zuverlässigkeitstheorie - Stochastischer Prozess Mathematisches Modell Reliability (Engineering) -- Mathematical models Stochastic processes Zuverlässigkeitstheorie (DE-588)4195525-0 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4195525-0 (DE-588)4057630-9 |
| title | Stochastic models in reliability |
| title_auth | Stochastic models in reliability |
| title_exact_search | Stochastic models in reliability |
| title_full | Stochastic models in reliability Terje Aven ; Uwe Jensen |
| title_fullStr | Stochastic models in reliability Terje Aven ; Uwe Jensen |
| title_full_unstemmed | Stochastic models in reliability Terje Aven ; Uwe Jensen |
| title_short | Stochastic models in reliability |
| title_sort | stochastic models in reliability |
| topic | Zuverlässigkeitstheorie - Stochastischer Prozess Mathematisches Modell Reliability (Engineering) -- Mathematical models Stochastic processes Zuverlässigkeitstheorie (DE-588)4195525-0 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Zuverlässigkeitstheorie - Stochastischer Prozess Mathematisches Modell Reliability (Engineering) -- Mathematical models Stochastic processes Zuverlässigkeitstheorie Stochastischer Prozess |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008526144&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000895226 |
| work_keys_str_mv | AT aventerje stochasticmodelsinreliability AT jensenuwe stochasticmodelsinreliability |