Dynamic Analysis of a 2-out-of-6:G Repairable System with Preventive Maintenance
- 1College of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, China
Abstract
This paper develops a 2-out-of-6:G repairable system with state-dependent preventive maintenance (PM) for functioning components. The 2-out-of-6:G configuration is adopted as a representative nontrivial case of the general k-out-of-n:G system, since it retains the essential features of component redundancy, multiple failure states, and a critical pre-failure state while remaining analytically tractable. When only two components remain functioning, PM is activated with probability β to reduce the risk of an immediate system breakdown caused by an additional failure. Using the supplementary variable method, the model is formulated as an abstract Cauchy problem. Within the C0-semigroup framework, the main operator is proved to generate a positive contraction C0-semigroup, ensuring the existence and uniqueness of a positive solution. By combining Greiner’s boundary perturbation method with spectral analysis, the strong convergence of the solution to the steady-state solution is established. Numerical simulations further illustrate the theoretical results and demonstrate the influence of preventive maintenance on system reliability performance.
Related
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BibTeX
@article{li2026dynamic,
title = {{Dynamic Analysis of a 2-out-of-6:G Repairable System with Preventive Maintenance}},
author = {Ruijuan Li and Ehmet Kasim},
journal = {Axioms},
year = {2026},
month = sep,
doi = {10.3390/axioms15100727},
url = {https://www.mdpi.com/2075-1680/15/10/727},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Dynamic Analysis of a 2-out-of-6:G Repairable System with Preventive Maintenance
AU - Ruijuan Li
AU - Ehmet Kasim
PY - 2026
DA - 2026/09/30
JO - Axioms
DO - 10.3390/axioms15100727
UR - https://www.mdpi.com/2075-1680/15/10/727
AB - This paper develops a 2-out-of-6:G repairable system with state-dependent preventive maintenance (PM) for functioning components. The 2-out-of-6:G configuration is adopted as a representative nontrivial case of the general k-out-of-n:G system, since it retains the essential features of component redundancy, multiple failure states, and a critical pre-failure state while remaining analytically tractable. When only two components remain functioning, PM is activated with probability β to reduce the risk of an immediate system breakdown caused by an additional failure. Using the supplementary variable method, the model is formulated as an abstract Cauchy problem. Within the C0-semigroup framework, the main operator is proved to generate a positive contraction C0-semigroup, ensuring the existence and uniqueness of a positive solution. By combining Greiner’s boundary perturbation method with spectral analysis, the strong convergence of the solution to the steady-state solution is established. Numerical simulations further illustrate the theoretical results and demonstrate the influence of preventive maintenance on system reliability performance.
SN - 2075-1680
ER -