基于重试机制与转换失效的k/(M+N): G系统可靠性建模与优化

doi:10.15960/j.cnki.issn.1007-6093.2024.04.004

Abstract

Abstract:

In this paper, the reliability and optimization model of repairable $k/(M+N):G$ retrial system with standby switching failure, Bernoulli vacation and working breakdown is established. It is assumed that when the working component fails, it is replaced by a warm standby component that has not yet failed. The replacement operation will lead to the failure of the warm standby component with a certain probability. In retrial space, the failed components follow the principle of random retrial. By using Runge-Kutta method and Cramer's rule, the transient and steady-state probabilities of the system are solved respectively, and the transient and steady-state reliability indexes and some other steady-state performance indexes of the system are obtained. Based on the defined cost elements and the steady-state performance indexes of the system, a minimization model of the total cost function per unit time is constructed, and the genetic particle swarm optimization (GA_PSO) hybrid algorithm is used to solve the optimization design model. The effects of different system parameters on the total cost function per unit time and steady-state performance index are evaluated by numerical experiments. The experimental results verify the reliability of the established model.

Key words: retrial, Bernoulli vacation, working breakdown, switching failure, reliability, optimization

CLC Number:

O213.2
O224

Jing LI, Linmin HU, Mingjia LI. Reliability modeling and optimization of k=(M+N): G system based on retrial mechanism and switching failure[J]. Operations Research Transactions, 2024, 28(4): 44-56.

Figures/Tables 6

References 27

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可靠性指标	$ A\left( {20} \right) $	$ m\left( {20} \right) $	$ A\left( \infty \right) $	$ M $	MUT	MDT
结果	0.993 0	0.004 0	0.991 2	0.004 7	212.518 8	1.890 6

其他各项稳态性能指标	$ {P_I} $	$ {P_B} $	$ {P_V} $	$ E\left( I \right) $	$ E\left( R \right) $	$ S.R. $
结果	0.359 9	0.194 4	0.445 7	1.439 1	1.647 2	0.003 6

$ \left( {\lambda , \alpha } \right) $	$ ({0.1, 0.4}) $	$ ({0.2, 0.4}) $	$ ({0.3, 0.4}) $	$ ({0.2, 0.5}) $	$ ({0.2, 0.6}) $
$ C\left( {\mu _b^ * , \mu _d^ * } \right) $	394.250 6	597.732 2	710.112 8	598.724 0	599.017 9
$ \mu _b^ * $	1.878 9	2.438 2	1.936 8	2.345 8	2.242 9
$ \mu _d^ * $	0.782 5	0.864 6	0.520 1	1.578 8	2.230 7
$ {P_I} $	0.278 5	0.128 0	0.071 9	0.127 1	0.126 3
$ {P_B} $	0.298 9	0.329 1	0.382 6	0.311 0	0.312 8
$ {P_V} $	0.422 6	0.542 9	0.545 5	0.561 9	0.560 9
$ S.R. $	0.003 2	0.002 3	0.000 7	0.002 3	0.002 2
$ E\left( I \right) $	1.772 7	3.770 1	5.016 0	3.777 3	3.784 1
$ E\left( R \right) $	1.329 5	0.400 8	0.066 8	0.396 2	0.392 3

$ \left( {\gamma , \delta } \right) $	$ ({2.0, 0.5}) $	$ ({3.0, 0.5}) $	$ ({4.0, 0.5}) $	$ ({3.0, 0.3}) $	$ ({3.0, 0.4}) $
$ C\left( {\mu _b^ * , \mu _d^ * } \right) $	394.250 6	387.141 1	383.428 2	489.931 0	426.880 7
$ \mu _b^ * $	1.878 9	1.855 0	1.839 6	1.820 1	1.875 7
$ \mu _d^ * $	0.782 5	0.780 9	0.784 5	0.693 6	0.754 3
$ {P_I} $	0.278 5	0.268 0	0.262 2	0.149 5	0.216 0
$ {P_B} $	0.298 9	0.305 5	0.309 4	0.260 1	0.284 1
$ {P_V} $	0.422 6	0.426 5	0.428 4	0.590 4	0.499 9
$ S.R. $	0.003 2	0.003 2	0.003 3	0.002 1	0.002 8
$ E\left( I \right) $	1.772 7	1.689 4	1.646 8	2.859 4	2.141 1
$ E\left( R \right) $	1.329 5	1.388 6	1.419 0	0.827 1	1.155 2

$ \Big( {\tilde \lambda , g} \Big) $	$ ({0.05, 0.4}) $	$ ({0.06, 0.4}) $	$ ({0.07, 0.4}) $	$ ({0.05, 0.5}) $	$ ({0.05, 0.6}) $
$ C\left( {\mu _b^ * , \mu _d^ * } \right) $	394.250 6	398.684 0	402.905 9	426.929 5	460.245 9
$ \mu _b^ * $	1.878 9	1.878 0	1.876 4	1.949 1	1.988 5
$ \mu _d^ * $	0.782 5	0.789 7	0.778 2	0.782 1	0.755 6
$ {P_I} $	0.278 5	0.266 7	0.255 7	0.221 4	0.171 9
$ {P_B} $	0.298 9	0.303 8	0.308 7	0.275 0	0.255 9
$ {P_V} $	0.422 6	0.429 5	0.435 6	0.503 6	0.572 2
$ S.R. $	0.003 2	0.003 1	0.003 0	0.002 8	0.002 3
$ E\left( I \right) $	1.772 7	1.833 6	1.892 8	2.141 1	2.521 5
$ E\left( R \right) $	1.329 5	1.279 9	1.231 8	1.115 6	0.905 3

$ \left( {q, \beta } \right) $	$ ({0.02, 2.0}) $	$ ({0.03, 2.0}) $	$ ({0.04, 2.0}) $	$ ({0.03, 2.5}) $	$ ({0.03, 3.0}) $
$ C\left( {\mu _b^ * , \mu _d^ * } \right) $	396.976 7	398.891 1	400.800 0	398.615 1	398.083 4
$ \mu _b^ * $	1.767 0	1.767 6	1.765 4	1.829 6	1.883 8
$ \mu _d^ * $	1.637 9	1.629 6	1.638 9	1.211 2	0.764 0
$ {P_I} $	0.274 3	0.272 1	0.269 7	0.273 3	0.274 2
$ {P_B} $	0.302 2	0.303 2	0.304 2	0.301 5	0.300 5
$ {P_V} $	0.423 5	0.424 8	0.426 0	0.425 2	0.425 3
$ S.R. $	0.006 2	0.009 3	0.012 3	0.009 3	0.009 4
$ E\left( I \right) $	1.800 5	1.822 0	1.843 5	1.817 0	1.814 2
$ E\left( R \right) $	1.308 3	1.293 7	1.279 0	1.298 5	1.301 5

Reliability modeling and optimization of k=(M+N): G system based on retrial mechanism and switching failure

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