Abstract
In this paper, we consider a two-unit parallel redundant system with deterioration on a lattice, where each unit has multi-stage deterioration levels, say, n levels. The transition from one deterioration level to the subsequent level occurs following the well-known Marshall-Olkin bivariate exponential distribution. We derive the closed form of the Laplace transform of the time to system failure in the two-unit parallel redundant system with deterioration on n×n lattice without repair and simultaneous failure, as well as the simple system on 3×3 lattice.
Highlights
Two-unit parallel redundant systems play a central role to design actual redundant component systems in terms of fault-tolerance
From the inductive argument, we derive the main results of this paper in the following: Theorem 4.1 In the two-unit parallel redundant system deteriorating on n × n lattice without repair and simultaneous failure, the Laplace transform of the time to system failure is by n−1
Corollary 4.2 In the two-unit parallel redundant system deteriorating on n × (n − 1) lattice without repair and simultaneous failure, the Laplace transform of the time to failure is P0(s)/(2a(s)), where P0(s) is given in Eq (61)
Summary
Two-unit parallel redundant systems play a central role to design actual redundant component systems in terms of fault-tolerance. Rinsaka and Dohi (2005) performed the behavioral analysis of a two-unit fault-tolerant software system with rejuvenation and formulated the system availability, where the number of degradation levels for each unit is two In this way, we note that the environmental diversity in software systems is based on the redundant configuration by either an identical replica of software or a non-identical hot standby system (Trivedi and Bobbio, 2017). Theorem 3.1: In the two-unit parallel redundant system with deterioration on 3 × 3 lattice, the Laplace transform of the time to system failure is given by. We simplify the assumptions on the repair and simultaneous failure
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