On the Use of Stochastic Processes in Modeling Reliability Problems

by Alessandro Birolini

Overview

Shastic 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 shastic 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.

Product Details

ISBN-13:	9783540156994
Publisher:	Springer Berlin Heidelberg
Publication date:	10/30/1985
Series:	Lecture Notes in Economics and Mathematical Systems , #252
Pages:	105
Product dimensions:	6.10(w) x 9.25(h) x 0.01(d)

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 Shastic 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.