On the Use of Stochastic Processes in Modeling Reliability Problems

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 -- 3.2 Alternating renewal processes -- 3.3 Markov processes with a finite state space -- 3.4 Semi-Markov processes with a finite state space -- 4 Applications to one-item repairable structures -- 4.1 Reliability function -- 4.2 Point-availability -- 4.3 Interval-reliability -- 4.4 Mission-oriented availabilities -- 4.5 Asymptotic behaviour -- 4.6 Stationary state -- 5 Applications to series, parallel, and series/parallel repairable structures -- 5.1 Series structures -- 5.2 1-out-of-2 redundancies -- 5.3 k-out-of-n redundancies -- 5.4 Series/parallel structures -- 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 -- 6.3 Influence of imperfect switching -- References.