Abstract
Aim. The introduction of the full paper reviews a number of papers on reliability models with dependent units in the open literature and proposes what we believe to be a new model mentioned in the title. The core of Section 1 consists of: (1) we present the assumptions of the circular Markov repairable systems with spatial dependence; (2) we put forward the Markov processes associated with the 4-unit and 5-unit circular Markov repairable systems with spatial dependence and define their states as indicated in Fig.1 and Fig. 2. Section 2 analyzes the state transitions of the 4-unit and 5-unit systems and obtains the state transition rate matrices corresponding to them. Section 3 discusses the instantaneous and asymptotic availabilities of the 4-unit and 5-unit systems, which are given by equations (3)-(5). Section 4 presents the numerical examples of the 4-unit and 5-unit systems. The curves of instantaneous availabilities are shown in Fig. 5 and Fig. 6. We obtain the conclusions that: (1) the system with independent units is more reliable than the circular Markov repairable system with spatial dependence; (2) the 5-unit circular Markov repairable system is more reliable than the 4-unit system.
Original language | English |
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Pages (from-to) | 923-928 |
Number of pages | 6 |
Journal | Xibei Gongye Daxue Xuebao/Journal of Northwestern Polytechnical University |
Volume | 32 |
Issue number | 6 |
State | Published - 1 Dec 2014 |
Keywords
- Availability
- Circular system
- Differential equations
- Inverse problems
- Laplace transforms
- Markov processes
- Markov repairable system
- Mathematical models
- MATLAB
- Matrix algebra
- Probability
- Reliability analysis
- Spatial dependence.