ABSTRACT

This paper studies a $K-out-of-N$$K-out-of-N$ retrial system with mixed standby components and a single repairman under Bernoulli vacation schedule. Such a model is motivated by some machine repair systems in practice. The repairman may either go for a vacation of random length with probability $p$$p$ or stay idle in system with probability $1-p$$1-p$ after the completion of a repair. If a component fails, it is repaired at once when the repairman is idle, whereas whether the repairman is busy or vacation, the failed components enter into an orbit. The expressions of steady-state availability, reliability function and the mean time to system first failure are obtained by using vector Markov process and Laplace transform theory. Sensitivity analysis and relative sensitivity analysis are provided. An application example of the intelligent automatic system is demonstrated. Finally, some numerical experiments are conducted to show the impacts of system parameters on reliability indexes. The results presented in the paper may be useful for machine repair system engineers.

摘要

本文研究了 $ķ-ØüŤ-ØF-ñ$$ķ-ØüŤ-ØF-ñ$伯努利休假时间表下具有混合备用组件和一名修理工的重试系统。在实践中，这种模型是由某些机器维修系统所激发的。修理工可能会随机休假$p$$p$ 或有可能闲置在系统中 $\mathrm{1个}-p$$\mathrm{1个}-p$维修完成后。如果某个组件发生故障，则在修理工空闲时立即对其进行维修，而无论修理工忙还是休假，发生故障的组件都会进入轨道。利用向量马尔可夫过程和拉普拉斯变换理论获得了稳态可用性，可靠性函数和系统首次出现故障的平均时间的表达式。提供了灵敏度分析和相对灵敏度分析。演示了智能自动化系统的一个应用实例。最后，进行了一些数值实验，以表明系统参数对可靠性指标的影响。本文中提出的结果可能对机器维修系统工程师有用。