Mathematical theory of reliability of time dependent systems with practical applications
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| Sprache: | English |
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1997
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| Schriftenreihe: | Wiley series in probability and statistics
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| 245 | 1 | 0 | |a Mathematical theory of reliability of time dependent systems with practical applications |c Igor N. Kovalenko ; Nickolaj Yu. Kuznetsov ; Philip A. Pegg |
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| adam_text | IMAGE 1
MATHEMATICAL THEORY OF
RELIABILITY OF TIME DEPENDENT SYSTEMS WITH PRACTICAL APPLICATIONS
IGOR N. KOVALENKO UNIVERSITY OF NORTH LONDON AND NATIONAL ACADEMY OF
SCIENCES OFTHE UKRAINA, KYIV, UKRAINA NICKOLAJ YU. KUZNETSOV V.M.
GLUSHKOV INSTITUTE OF CYBERNETICS, KYIV, UKRAINA PHILIP A. PEGG
UNIVERSITY OF NORTH LONDON
JOHN WILEY & SONS CHICHESTER * NEW YORK * WEINHEIM * BRISBANE *
SINGAPORE * TORONTO
IMAGE 2
CONTENTS
PREFACE XI
1 INTRODUCTION 1
1.1 INTRODUCTORY REMARKS 1
1.2 CONTEXT 2
1.3 BASIC MATHEMATICAL CONCEPTS OF RELIABILITY 4
1.4 NON-REPAIRABLE SYSTEMS 6
1.5 REPAIRABLE SYSTEMS 15
1.6 ALTERNATIVE MODEIS FOR THE RELIABILITY OF SYSTEMS 17
1.7 QUALITY CONTROL AND IMPROVEMENT AND RELIABILITY 21
1.8 STATISTICAL INFERENCE OF RELIABILITY PARAMETERS 23
1.9 MONTE CARLO METHODS 23
1.10 CONTENTS OF THIS BOOK 24
REFERENCES 26
2 MARKOV AND SEMI-MARKOV MODELS AS A BASIS FOR THE MATHEMATICAL ANALYSIS
OF SYSTEM RELIABILITY 27
2.1 REVIEW OF SOME RELEVANT PROBABILITY CONCEPTS 27
2.2 MARKOV PROCESSES 30
2.3 SEMI-MARKOV PROCESS (SMP) 40
2.4 MARKOV MODEIS OF SYSTEMS WITH DISCRETE EVENTS 44
2.5 SEMI-MARKOV MODEIS OF SYSTEMS WITH DISCRETE EVENTS 45
2.6 IMPORTANT SPECIAL CASES 48
REFERENCES 53
3 METHODS FOR INVESTIGATING HOMOGENEOUS AND NON-HOMOGENEOUS POINT
PROCESSES (EVENT FLOWS) 55
3.1 POINT PROCESSES 55
3.2 ERGODICITY 57
3.3 THE /C-INTENSITY OF THE POINT PROCESS 58
3.4 EQUILIBRIUM EQUATIONS 60
3.5 APPLICATION TO SEMI MARKOV PROCESSES 61
3.6 FURTHER ERGODIC RELATIONS 62
3.7 REGENERATIVE MODEIS FOR FAILURE FLOWS 64
3.8 THE MAIN RELIABILITY PARAMETERS VIA POINT PROCESS PARAMETERS 69
REFERENCES 73
4 FAULT TREES -THE CURRENT STATE OF RESEARCH 75
4.1 INTRODUCTION 75
4.2 MAIN DEFINITIONS AND NOTATIONS 76
4.3 SYSTEM RELIABILITY ANALYSIS USING FAULT TREES 79
4.4 PROBABILITY EVALUATION OF FAULT TREES 81
IMAGE 3
VLLL CONTENTS
4.5 FAULT TREE EVALUATION BASED ON MINIMAL CUT SETS 84
4.6 PROBLEMS ARISING IN CUT SET EVALUATION FOR LARGE FAULT TREES 88
4.7 A MULTI-LEVEL REPRESENTATION OF A FAULT TREE CONTAINING REPLICATED
GATES 89
4.8 DESCRIPTION OF GATE AND COMPONENT TYPES 96
4.9 FAMOCUTN-ANALYTICAL EVALUATION OF MAIN MODULE CUT SETS 96
4.10 EXAMPLES 103
REFERENCES 107
BIBLIOGRAPHY 109
5 THEORY OF REDUNDANT SYSTEMS 111
5.1 PRELIMINARY REMARKS 111
5.2 FINITE VARIATES ANALYSIS 112
5.3 BUSY PERIOD ANALYSIS: ANALYTICAL EXPRESSIONS 113
5.4 SMALL PARAMETER ANALYSIS OF BUSY PERIOD VARIABLES 118
5.5 FAILURE PROBABILITY WITHIN A BUSY PERIOD THROUGH HYPER-ERLANGIAN
APPROXIMATION 125
5.6 TIME-VARYING RELIABILITY PARAMETERS VIA BUSY PERIOD PARAMETERS 128
REFERENCES 130
BIBLIOGRAPHY 132
6 MONTE CARLO METHODS 133
6.1 RANDOM VARIABLE GENERATION 133
6.2 MODELLING OF A NON-HOMOGENEOUS POISSON PROCESS 140
6.3 MODELLING OF A MARKOV CHAIN IN CONTINUOUS TIME 141
6.4 MODELLING OF SEMI-MARKOV PROCESSES 141
6.5 ACCURACY OF ESTIMATORS AND THE NECESSARY NUMBER OF REALISATIONS 143
6.6 APPLICATIONS TO RELIABILITY PROBLEMS 148
REFERENCES 152
BIBLIOGRAPHY 153
7 RELIABILITY ANALYSIS USING PERTURBATION METHODS 155
7.1 INTRODUCTORY REMARKS 155
7.2 THE PROBLEM FOR MARKOV RELIABILITY MODEIS 158
7.3 LIGHT TRAFFIC LIMITS 160
7.4 PHASE-TYPE AND MATRIX-EXPONENTIAL APPROXIMATIONS 162
7.5 INFINITESIMAL PERTURBATION ANALYSIS 164
REFERENCES 167
BIBLIOGRAPHY 167
8 STIFF PROCESSES IN RELIABILITY ANALYSIS 169
8.1 INTRODUCTION REMARKS 169
8.2 SMALL PARAMETERS IN DIFFERENTIAL EQUATIONS (REGULAER CASE) 170
8.3 SMALL PARAMETERS IN DIFFERENTIAL EQUATIONS (SINGULAR CASE) 172
8.4 THE SADDLE POINT METHOD 174
8.5 ASYMPTOTIC AGGREGATION OF STATES OF SEMI-MARKOV PROCESS 176
8.6 MODELS OF PROCESSES IN DIFFERENT SCALES 181
8.7 USE OF THE INVARIANCE PRINCIPLE 186
8.8 SOME TECHNIQUES FOR THE INTRODUCTION OF A SMALL PARAMETER INTO
STOCHASTIC RELATIONS 186
IMAGE 4
CONTENTS
IX
REFERENCES 190
BIBLIOGRAPHY 190
9 VARIANCE REDUCTION METHODS 193
9.1 INTRODUCTION 193
9.2 IMPORTANCE SAMPLING 195
9.3 STRATIFIED SAMPLING 203
9.4 CONTROL VARIABLE SAMPLING 206
9.5 METHOD OF ANTITHETIC VARIABLES 209
9.6 COMMON RANDOM NUMBERS TECHNIQUE 210
9.7 ANALYTICAL-STATISTICAL METHODS 210
9.8 SOME ESTIMATES FOR SYSTEMS DESCRIBED BY REGENERATIVE PROCESSES 213
REFERENCES 215
BIBLIOGRAPHY 218
10 ANALYTICAL-STATISTICAL METHODS FOR RAPID SIMULATION OF REPAIRABLE
SYSTEMS WITH STRUCTURE REDUNDANCY 221
10.1 INTRODUCTION 221
10.2 RAPID SIMULATION OF M OUT OF N STRUCTURES 222
10.3 BOUNDED COEFFICIENT OF VARIATION FOR HIGHLY RELIABLE SYSTEMS 228
10.4 EXAMPLES 232
10.5 THE ANALYTICAL-STATISTICAL METHOD FOR THE EVALUATION OF THE
RELIABILITY OF REPAIRABLE SYSTEMS 240
10.6 EVALUATION OF NON-STATIONARY STATE PROBABILITIES OF ALTERNATING
RENEWAL PROCESSES 246
10.7 ANALYTICAL-STATISTICAL METHOD FOR THE EVALUATION OF THE SOJOURN
TIME DISTRIBUTION FOR A MARKOV PROCESS 251
10.8 EVALUATION OF THE UNAVAILABILITY OF REPAIRABLE SYSTEMS 254
REFERENCES 261
11 MEASURES OF RELIABILITY IMPORTANCE OF COMPONENTS 263
11.1 THE PURPOSE OF IMPORTANCE MEASURES 263
11.2 BIRNBAUM IMPORTANCE OF COMPONENTS 264
11.3 SOME GENERALISATIONS OF THE BIRNBAUM MEASURE 268
11.4 VESELY-FUSSELL COMPONENT IMPORTANCE MEASURE 270
11.5 BARLOW-PROSCHAN IMPORTANCE OF COMPONENTS 273
11.6 NATVIG IMPORTANCE MEASURES 277
11.7 IMPORTANCE OF MODULES AND CUT SETS 281
11.8 METHODS FOR EVALUATING RELIABILITY IMPORTANCE 285
11.9 INCREASE OF SYSTEM RELIABILITY BY PARALLEL REDUNDANCY AND COMPONENT
IMPROVEMENT 288
11.10 CONCLUDING REMARKS 294
REFERENCES 295
BIBLIOGRAPHY 296
INDEX 299
|
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| author | Kovalenko, Igorʹ N. 1934-2019 Kuznecov, Nikolaj Ju Pegg, Philip A. |
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| spellingShingle | Kovalenko, Igorʹ N. 1934-2019 Kuznecov, Nikolaj Ju Pegg, Philip A. Mathematical theory of reliability of time dependent systems with practical applications Betrouwbaarheid gtt Fiabilité - Modèles mathématiques ram Machines gtt Markov, Processus de ram Wiskundige modellen gtt Mathematisches Modell Reliability (Engineering) -- Mathematical models Markov processes Reliabilität (DE-588)4213628-3 gnd |
| subject_GND | (DE-588)4213628-3 |
| title | Mathematical theory of reliability of time dependent systems with practical applications |
| title_auth | Mathematical theory of reliability of time dependent systems with practical applications |
| title_exact_search | Mathematical theory of reliability of time dependent systems with practical applications |
| title_full | Mathematical theory of reliability of time dependent systems with practical applications Igor N. Kovalenko ; Nickolaj Yu. Kuznetsov ; Philip A. Pegg |
| title_fullStr | Mathematical theory of reliability of time dependent systems with practical applications Igor N. Kovalenko ; Nickolaj Yu. Kuznetsov ; Philip A. Pegg |
| title_full_unstemmed | Mathematical theory of reliability of time dependent systems with practical applications Igor N. Kovalenko ; Nickolaj Yu. Kuznetsov ; Philip A. Pegg |
| title_short | Mathematical theory of reliability of time dependent systems with practical applications |
| title_sort | mathematical theory of reliability of time dependent systems with practical applications |
| topic | Betrouwbaarheid gtt Fiabilité - Modèles mathématiques ram Machines gtt Markov, Processus de ram Wiskundige modellen gtt Mathematisches Modell Reliability (Engineering) -- Mathematical models Markov processes Reliabilität (DE-588)4213628-3 gnd |
| topic_facet | Betrouwbaarheid Fiabilité - Modèles mathématiques Machines Markov, Processus de Wiskundige modellen Mathematisches Modell Reliability (Engineering) -- Mathematical models Markov processes Reliabilität |
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