Reliability of Several Standby-Priority-Redundant Systems

Abstract

This paper develops 3 models for standby redundant systems consisting of dissimilar units. In an effort to increase system reliability, priorities are assigned to operating the units as well as for repair in one repair facility. A 1-out-of-3:G system is considered in models 1 and 2. The operating schedule is fixed in the order top, middle, and low prioritics which are assigned to the 3 units. The effect on system reliability of choosing two repair disciplines viz., 1) Head-of-line (Model 1), and 2) Preemptive-resume (Model 2), is studied. Markov renewal processes are used for the head-of-line, and the Supplementary variable technique for the preemptive-resume repair discipline. The distribution of time to system failure and its mean are derived. In model 3, a 1-out-of-2:G system is considered in which the priority unit (unit 1) is subject to both repair and preventive maintenance while only repair is considered for unit 2. Expressions for the Laplace transforms of the various state probabilities, the availability, and the steady-state availability have been obtained by using the supplementary variable technique.