Reliability and Availability of Repairable Systems

Abstract

Reliability and availability analysis of repairable systems is generally performed using stochastic processes, including Markov, semi-Markov, and semi-regenerative processes. The mathematical foundation of these processes is in Appendix A7. Equations used to investigate Markov and semi-Markov models are summarized in Table 6.2. This chapter investigates systematically most of the reliability models encountered in practical applications. Reliability figures at system level have indices Si (e. g. MITFsi ), where S stands for system and i is the state entered at t = 0 (Table 6.2). After Section 6.1 (introduction, assumptions, conclusions), Section 6.2 investigates the one-item structure under general conditions. Sections 6.3 - 6.6 deal extensively with series, parallel, and series-parallel structures. To unify models and simplify calculations, it is assumed that the system has only one repair crew and no further failures occur at system down. Starting from constant failure and repair rates between successive states (Markov processes), generalization is performed step by step (beginning with the repair rates) up to the case in which the process involved is regenerative with a minimum number of regeneration states. Approximate expressions for large series - parallel structures are investigated in Section 6.7. Sections 6.8 considers systems with complex structure for which a reliability block diagram often does not exist. On the basis of practical examples, preventive maintenance, imperfect switching, incomplete coverage, elements with more than two states, phased-mission systems, common cause failures, and general reconfigurable fault tolerant systems with reward & frequency / duration aspects are investigated. Basic considerations on network reliability are given in Section 6.8.8 and a general procedure for complex structures is in Section 6.8.9. Sections 6.9 introduces alternative investigation methods (dynamic FTA, BDD, event trees, Petri nets, computer-aided analysis), and gives a Monte Carlo approach useful for rare events. Asymptotic & steady-state is used as a synonym for stationary (pp. 490 & 501). Results are summarized in tables. Selected examples illustrate the practical aspects.