On the use of stochastic processes in modeling reliability problems
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Bibliographic Information
On the use of stochastic processes in modeling reliability problems
（Lecture notes in economics and mathematical systems, 252）
Springer-Verlag, c1985
- : Germany
- : U.S.
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Includes index
Description and Table of Contents
Description
Stochastic processes are powerful tools for the investigation of reliability and availability of repairable equipment and systems. Because of the involved models, and in order to be mathematically tractable, these processes are generally confined to the class of regenerative stochastic processes with a finite state space, to which belong: renewal processes, Markov processes, semi-Markov processes, and more general regenerative processes with only one (or a few) regeneration staters). The object of this monograph is to review these processes and to use them in solving some reliability problems encountered in practical applications. Emphasis is given to a comprehensive exposition of the analytical procedures, to the limitations in volved, and to the unification and extension of. the models known in the literature. The models investigated here assume. that systems have only one repair crew and that no further failure can occur at system down. Repair and failure rates are general ized step-by-step, up to the case in which the involved process is regenerative with only one (or a few) regeneration state(s). Investigations deal with different kinds of reliabilities and availabilities for series/parallel structures. Preventive main tenance and imperfect switching are considered in some examples.
Table of Contents
1 Introduction and summary.- 2 Basic concepts of reliability analysis.- 2.1 Mission profile, reliability block diagram.- 2.2 Failure rate.- 2.3 Reliability function, MTTF, MTBF.- 2.4 More general considerations on the concept of redundancy.- 2.5 Failure mode analysis and other reliability assurance tasks.- 3 Stochastic processes used in modeling reliability problems.- 3.1 Renewal processes.- 3.1.1 Definition and general properties.- 3.1.2 Renewal function and renewal density.- 3.1.3 Forward and backward recurrence-times.- 3.1.4 Asymptotic and stationary behaviour.- 3.1.5 Poisson process.- 3.2 Alternating renewal processes.- 3.3 Markov processes with a finite state space.- 3.3.1 Definition and general properties.- 3.3.2 Transition rates.- 3.3.3 State probabilities.- 3.3.4 Asymptotic and stationary behaviour.- 3.3.5 Summary of important relations for Markov models.- 3.4 Semi-Markov processes with a finite state space.- 3.4.1 Definition and general properties.- 3.4.2 At t = 0 the process enters the state Zi.- 3.4.3 Stationary semi-Markov processes.- 3.5 Regenerative stochastic processes.- 3.6 Non-regenerative stochastic processes.- 4 Applications to one-item repairable structures.- 4.1 Reliability function.- 4.2 Point-availability.- 4.3 Interval-reliability.- 4.4 Mission-oriented availabilities.- 4.4.1 Average-availability.- 4.4.2 Joint-availability.- 4.4.3 Mission-availability.- 4.4.4 Work-mission-availability.- 4.5 Asymptotic behaviour.- 4.6 Stationary state.- 5 Applications to series, parallel, and series/parallel repairable structures.- 5.1 Series structures.- 5.1.1 Constant failure and repair rates.- 5.1.2 Constant failure rates and arbitrary repair rates.- 5.1.3 Arbitrary failure and repair rates.- 5.2 1-out-of-2 redundancies.- 5.2.1 Constant failure and repair rates.- 5.2.2 Constant failure rates and arbitrary repair rate.- 5.2.3 Influence of the repair times density shape.- 5.2.4 Constant failure rate in the reserve state, arbitrary failure rate in the operating state, and arbitrary repair rates.- 5.2.4.1 At t = 0 the system enters the regeneration state, Z1.- 5.2.4.2 At t= 0 the system enters the state Z0.- 5.2.4.3 Solution for some particular cases.- 5.3 k-out-of-n redundancies.- 5.3.1 Constant failure and repair rates.- 5.3.2 Constant failure rates and arbitrary repair rate.- 5.4 Series/parallel structures.- 5.4.1 Constant failure and repair rates.- 5.4.2 Constant failure rates and arbitrary repair rate.- 6 Applications to repairable systems of complex structure and to special topics.- 6.1 Repairable systems having complex structure.- 6.2 Influence of preventive maintenance.- 6.2.1 One-item repairable structures.- 6.2.2 1-out-of-2 redundancy with hidden failures.- 6.3 Influence of imperfect switching.- References.
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