Reliability Modeling And Analysis Of Consecutive K/n:F Retrial Systems Based On Different Characteristics

Redundancy design is an efficient technique that can be used to improve and increase the reliability of systems in engineering practice.The consecutive k/n:F system,as atypical form of redundancy,has been extensively applied in industry and system design.Recently,the reliability of repairable k/n retrial systems has attracted the attention of scholars,but little work has been conducted to consider the retrial feature in the reliability modeling and evaluation of more complex consecutive k/n:F systems.Therefore,this paper develops the mathematical models for reliability of the consecutive k/n:F retrial system with different characteristics according to the actual problems,and investigates the reliability and costeffectiveness of the developed models.Firstly,a linear consecutive k/n:F retrial system model with an unreliable repair facility is analyzed,in which preventive maintenance(PM)and repair for working breakdowns are considered for the repair facility.All the random variables in the system are assumed to follow an exponential distribution.Based on the repair priority of key components and retrial principle,the reliability indexes and the cost function per unit time of the system are obtained by employing Markov process theory,matrix analytical method and so on.Numerical experiments are executed to discuss the variation of reliability indexes with system parameters,the optimal design of the cost-effectiveness ratio,and the influence of PM on steady-state availability and cost-effectiveness ratio.It has been found that if managers want to improve the reliability of the system,they can properly control the occurrence and ending rate of PM for the repair facility.Secondly,a linear consecutive k/n:F retrial system model with two-phase repair is investigated,where failure may occur to all non-failed components even though the system has failed.The repairman provides the first essential repair and the second optional repair for each failed component.All random variables are assumed to be exponentially distributed.Based on the state transition of the system,the reliability indexes and cost-effectiveness ratio of the system are evaluated by using Markov process theory,matrix analytical method and Runge-Kutta technique.Numerical examples are presented to discuss the effect of system parameters on the reliability indexes.The optimal value of cost-effectiveness ratio function per unit time is provided numerically as well.It has been found that the reliability can be improved by increasing the repair rate or retrial rate of the failed components.Finally,a linear consecutive k/n:F retrial system model with two-phase repair and Bernoulli vacation is developed.After completing the repair of a failed component,the repairman either leaves for a vacation or remains idle in the system.Suppose that the phasetype distribution governs the repair time of each phase,and other random variables are all exponentially distributed.Based on the divided state sets,the state transition rate matrix of the system is presented.Several system reliability indexes under transient and steadystate are obtained by means of the Markov process theory,matrix analytical method and the technique of solving differential equations.Numerical experiments outline how reliability indexes and cost-effectiveness ratio are affected by system parameters.The system models with and without vacation in terms of cost-effectiveness ratio are compared numerically as well.It has been found that a reasonable vacation rate for the repairman can be set to reach the goal of minimizing the cost-effectiveness ratio.