Reliability Analysis Of Multi-stage Shock Degradation And Self-healing System Based On Markov Update Process

In the reliability theory,the research on damage is always a hot spot.Aiming at the dependence between random shocks and system degradation,and the self-healing phenomenon of damage,this paper mainly contains two aspects.on the one hand,as two main kinds of common damage,random shocks(such as abrupt change of mechanical stress,temperature and voltage etc.),system degradation(such as wear,erosion etc.)and dependence relationship between them often existed simultaneously in many systems.Due to the dependence,a host of characteristics of multi-stage of system is emerged.In this paper,an innovative composite model of n-stage random shocks and m-stage degradation(model 1)has been developed.By this model,the mutual dependence and multi-stage characteristics of them has been analyzed effectively,which has great significance to improve the accuracy of the existing model of random shocks or system degradation.Moreover,the model 1 has extended the existing models of two-stage of random shocks or system degradation,and described a more generalized interdependency between the random shocks and degradation.namely,both of them contribute to system damage accumulation and then the system stage changed when damage accumulation reaches a pre-set threshold.In turn,the various parameters of system's following shocks arriving process and degradation,such as intension of shocks arriving,damage value of single shock and rate of deterioration,are feedback controlled by the state transition.Furthermore,the method of applying of several general degradation modeling,such as linear path degradation,Inverse Gaussian model and Gamma deterioration,into modell has been analyzed in this paper.On the other hand,in the field of engineering and materials,more and more researches focus on the damage self-healing.In some way,system's capability of damage self-healing reflects its higher levels of intelligence and automation,which has many obvious advantages such as system's life prolonging and low human intervention etc.It is obvious that damage self-healing has a significant impact on the damage accumulation of the self-healing system,thus affecting the life and reliability of the system.Therefore,it is significant to consider the influence of self-healing mechanism in the reliability modeling of the self-healing system for the model accuracy.At present,there are few reliability theories related to self-healing systems.With the rapid development of self-healing systems,the reliability modeling of various self-healing mechanisms needs to be further developed,and the research in this field is in great demand and highly innovative.Inspired by practical cases,due to conservation of energy and quality,the system's self-healing behavior without outside intervention is limited generally.In order to describe the restriction,in this paper,the damage healing amount is introduced,with the damage accumulation,which construct a competing failure of self-healing ability(model 2).Namely,self-healing mechanism fails once one of them reaches pre-set threshold,and then the damage only accumulates without recovering,of course,then the system may be still working until total failure.By constructing a Markov renewal process with two-dimensional state space,this model has traced the paths of the two dependent variables of damage process simultaneously.The subject and solution of this model is novel.For reliability modeling on the two subjects above,via discrete state method,the analytic expression of semi Markov nuclear has been obtained,and the Markov renewal process has been constructed.Through the Laplace transform and its numerical inversion,the renewal equations can be successfully solved.And several closed-form solutions of reliability index have been given.Finally,via numerical examples,effectiveness of conclusions of this paper has been illustrated.