Abstract
The paper provides reliability analysis of a cold double redundant renewable system assuming that both life-time and repair time distributions are arbitrary. The proposed approach is based on the theory of decomposable semi-regenerative processes. We derive the Laplace–Stieltjes transform of two main reliability measures like the distribution of the time between failures and the time to the first failure. The transforms are used to calculate corresponding mean times. It is further derived in closed form the time-dependent and time stationary state probabilities in terms of the Laplace transforms. Numerical results illustrate the effect of the type of distributions as well as their parameters on the derived reliability and probabilistic measures.
Highlights
The use of parallel or redundant units is an often recommended way of increasing the system reliability
In the last few decades, many authors have studied the redundant systems under different sets of assumptions about the system’s attributes and level of generality, the distribution of life, and repair times when one or more units are standby
We formulate the model where both of distributions are assumed to be arbitrary. Such models are interesting both from theoretical and practical points of view. These studies are related to the creation and development of new mathematical methods such as regenerative methods, especially methods of the Decomposable Semi-Regenerative Processes (DSRP), and Markovization methods via introduction of the supplementary variables
Summary
The use of parallel or redundant units is an often recommended way of increasing the system reliability. One possible generalization is to combine Smith’s idea with a semi-Markov approach [2], which seems quite appropriate for real models The result of such combination is a semi-regenerative process. In paper [13], the authors investigated a model of a polling system by means of the DSRP Another approach related to the study of complex systems (proposed in Belyaev [14]) contains the introduction of so-called supplementary variables. According to this method, the original model can be described by a continuous-time Markov chain (Markovization method).
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