Reliability Modeling And Optimization For K/n:G Retrial Systems With Unreliable Repair Equipment

Redundancy design is an important means to improve system reliability and availability.Various redundant system models have been studied by many scholars,including cold,warm and hot standby systems and k/n:G systems.The k/n:G system is a kind of redundancy model with universal applicability in practical engineering.In recent years,reliability modeling and optimization of redundant repairable systems based on retrial feature and unreliable repair equipment have attracted the attention of some scholars in reliability theory research,but there are still some new problems that need to be further researched.Because of this,based on the unreliable repair equipment and retrial of failed components,this paper develops an extended study of the k/n:G repairable system,deduces the reliability indexes of the extended models such as availability,reliability function and the mean time to first failure,and the optimization design problems of the extended models are analyzed.Firstly,the reliability model of repairable k/n:G retrial system with standby switching failure,Bernoulli vacation and working breakdown is established.When the system 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.When a component fails,if the repair equipment is in a state of busy or on vacation,the failed component enters into a virtual retrial space and tries again after a period of time until the retrial succeeds and the component is repaired.The Runge-Kutta method and Laplace transform method are adopted to evaluate the instantaneous availability,instantaneous failure frequency,reliability function and the mean time to first failure of the system.Based on the definition of system state,the steady-state probability equations of the system are established,and some steady-state reliability indexes of the system are obtained.The influence of each parameter on steady-state failure frequency and reliability function is given by numerical examples,and the sensitivity and relative sensitivity of steady-state availability and the mean time to first failure are analyzed.Secondly,the reliability model of repairable k/n:G retrial system with two failure modes,preventive maintenance and unreliable repair equipment is established.All components in the system have two failure modes,mode a failure and mode b failure.The failure time,repair time and retrial time of all components in the system are assumed to obey exponential distribution.The single repair equipment may be subject to breakdown in a busy period.The failure and repair times of the repair equipment follow the exponential distribution.The idle repair equipment will be performed preventive maintenance,and the duration of preventive maintenance follows an exponential distribution.The Markov process theory and matrix analysis method are employed to derive the steady-state probabilities and the steady-state availability of the system.The Laplace transform method is utilized to calculate the reliability function and the mean time to first failure of the system.To verify the correctness of the model,numerical analysis is executed to demonstrate the impact of each parameter on system steady-state availability,reliability function and the mean time to first failure.Finally,the optimization model of repairable k/n:G system with unreliable repair equipment and retrial of failed components is established.Based on the steady-state probability derived in Chapter 2 and Chapter 3,the system performance indexes related to the defined cost elements are obtained,and the minimization models of total cost function per unit time of two different systems are constructed.The hybrid genetic-particle swarm algorithm is used to solve the optimization models of different systems by numerical examples.