Probabilistic Analysis of Redundant Systems (Lecture Notes in Economics and Mathematical Systems, 175)

Srinivasan, S.K.; Subramanian, R.

ISBN 10: 3540097368 / ISBN 13: 9783540097365

Editore: Springer, 1980

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Titolo: Probabilistic Analysis of Redundant Systems ...

Casa editrice: Springer

Data di pubblicazione: 1980

Legatura: Brossura

Condizione: New

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Riassunto:

Reliability theory has become one of the important areas in Operational Research and Systems Engineering. Any system analysis, in order to be complete, must give due consideration to system reliability and availability. A system deSigner is often faced with the problems of evaluation and improvement of system relia­ bility and determination of optimum preventive maintenance schedule. In the solution of these problems, he is largely aided by mathematical mOdels. These models have received consi­ derable attention in the past several years following the satel­ lite era. The monographs of Gnedenko, Belyayev and Solovyev, and Barlow and Proschan describe the state of art of the subject upto 1965 and are largely responsible for the further work in the subject. The large number of papers and surveys that have appeared subsequently in journals devoted to Operational Research, Industrial Engineering and Statistical Quality Control amply demonstrate the overwhelming importance of the subject in contexts other than satellite and space craft research. While there are very many important problems that stem from these models, atten­ tion has been largely confined to calculations of reliability of the system. In a lighter vein the authors feel that the original papers in the area have a common feature-oBJECTIVE ORIENTEDNES- the general theme of Operational Research and in general, it is carried too far and to a high degree of meticulousness. Thus there is a general need for a cogent account of all the results that have appeared in the literature.

Contenuti:

1 Redundant Systems.- 1.1 Introduction.- 1.2 Repairable Systems.- 1.3 2-Unit Standby Redundant Systems.- 1.4 Parallel Redundant System.- 1.5 Multiple Unit Systems.- 1.6 Gnedenko Systems.- 1.7 Systems with Imperfect Switchover.- 1.8 Priority Redundant Systems.- 1.9 Intermittently Used Systems.- 1.10 Optimization Problems in Reliability.- 1.11 Scope of the Present Work.- 2 Renewal Theory and Point Processes.- 2.1 Introduction.- 2.2 Renewal Process.- 2.3 Stationary Point Processes.- 2.4 Special Point Processes.- 2.4a Stationary Renewal Processes.- 2.4b Alternating Renewal Processes.- 2.4c Markov Renewal Processes.- 2.5 Regenerative Processes.- 2.6 Multivariate Point Processes.- 3 Cold Standby Systems.- 3.1 Introduction.- 3.2 Reliability Analysis.- 3.3 Availability Analysis.- 3.4 Multivariate Point Process of the Events Ei.- 3.5 Steady State Characteristics.- 3.6 Visits to Different States and Sojourn times.- 3.7 Special Cases.- 3.7a Lifetime Exponentially Distributed.- 3.7b Repair Time Exponentially Distributed.- 3.8 Cold Standby System of Dissimilar Units.- 4 Warm Standby System.- 4.1 Introduction.- 4.2 Reliability and Availability Analysis.- 4.3 Characterization of events.- 4.4 Steady State Characteristics.- 4.5 Dissimilar Units 92.- 4.6 Special Cases.- 4.7 Numerical Results.- 5 Warm Standby Systems with an Imperfect Switchover.- 5.1 Introduction.- 5.2 Problem Description and Notation.- 5.3 Reliability Analysis.- 5.4 Availability Analysis.- 5.5 A System of Dissimilar Units.- 5.5a Reliability Analysis.- 5.5b Availability Analysis.- 5.6 System with Identical Units.- 5.6a Reliability Analysis.- 5.6b Availability Analysis.- 5.7 Numerical Results.- 6 Warm Standby Systems with an Imperfect Switchover and a Single Repair Ficitity.- 6.1 Introduction.- 6.2 General Analysis.- 6.3 Reliability Analysis.- 6.4 Availability Analysis.- 6.5 The Effect of Preemptive Priorities in Service on Reliability Measures.- 6.6 System with Dissimilar Units.- 6.7 Numerical Results.- 7 Intermittently Used Cold Standby Systems.- 7.1 Introduction.- 7.2 Formulation of the Problem.- 7.3 One Unit System with a Repair Facility.- 7.4 Two Unit System with Single Repair Facility.- 7.5 Numerical Results 201.- 7.5a One Unit System.- 7.5b Two Unit System.- 8 Intermittently Used Two Unit Systems: Warm Standby Redundancy.- 8.1 Introduction.- 8.2 Formulation of the Problem.- 8.2a P.d.f. of the Time to the First D-event.- 8.2b Mean Number of D-events.- 8.2c Mean Square Number of D-events.- 8.2d Duration of Disappointment.- 8.3 A System of Dissimilar Units: Standby under Perpetual Vigil.- 8.3a P.d.f. of the Time to the First D-event.- 8.3b Mean Number of D-events.- 8.3c Mean Square Number of D-events.- 8.3d Expected Duration of Disappointments.- 8.3e Special Cases.- 8.4 Warm Standby Redundancy in which Failures are Detected only During Need Periods.- 8.4a Behaviour of the Sub-system in Standby.- 8.4b Stochastic Process of a-events.- 8.4c Stochastic Process of D-events.- 8.4d Duration of Disappointment.- 8.4e Special Cases.- 9 Priority Standby Redundant Systems.- 9.1 Priority Systems.- 9.2 The Model.- 9.3 Analysis of the Model.- 9.4 Preemptive Repair.- 9.4a Reliability Analysis.- 9.4b Availability Analysis.- 9.5 Nonpreemptive Repair.- 9.5a Reliability Analysis.- 9.5b Availability Analysis.- 9.6 Cold Standby System.- 9.6a Preemptive Repair.- 9.6b Nonpreemptive Repair.- 9.7 Optimization Model.- 9.8 Numerical Results.- 10 Multicomponent Systems.- 10.1 Introduction.- 10.2 Model 1: Single Repair Facility.- 10.2a System Description 290.- 10.2b The Birth and Death Process Associated with the Spares.- 10.2c Time to System Failure (TSF).- 10.2d Availability Analysis.- 10.3 Model 2: r-repair Facilities.- 10.3a System Description 297.- 10.3b The Birth and Death Process Associated with the Spares.- 10.3c Time to System Failure.- 10.3d Availability Analysis.- 10.4 Explicit Solution for the case m=2 and r=l.- 10.5 Explicit Solution for the Case m=5 and r=3.- 10.6 Numerical Results.- 10.7 Optimization Problems.- 10.8 n-unit System with Arbitrary Repair Rate.- 10.8a Reliability Analysis.- 10.8b Availability Analysis.- 10.8c The 3-unit System.- 10.9 Grnedenko Systems.- 10.9a Reliability Analysis.- 10.9b Availability Analysis.- 10.9c A More General Model.- References.- Author Index.