Reliability Analyzing For Systems With Mutually Dependent Competing Failure Processes

With the development of modern technology,more and more large-scale complex systems are putting into use in engineering.These systems are usually affected by two types of failure processes in operation,which are respectively soft failure process caused by internal degradation of the system and hard failure process caused by external shock.Soft failure refers to the failure of the system when the system degradation exceeds a certain failure threshold,while hard failure refers to the failure of the system when the external shock exceeds a critical threshold.Whether soft or hard failure occurs,the system will fail to work.Because of the interaction between the external shock process and degradation process of the system,the two types of failures of the system constitute mutually dependent competing failure processes.In this paper,three types of classical shock models and two generalized mixed shock models are considered under the framework of mutually dependent competing failure processes.We not only study the reliability calculation problem for the single-component system with mutually dependent competing failure processes,but also investigate the reliability calculation problem for the multi-component complex systems under random shock environment.To deal with the dependency between soft failure and hard failure,this paper uses the method of calculating the jointed survival probability of soft and hard failure to derive the system reliability.This method not only improves the accuracy of reliability evaluation,but also greatly reduces the complexity of calculation.The main research results and innovations are as follows:Firstly,under the assumptions that internal degradation has a linear degradation path and the arrival of external shocks follows the Poisson process,the reliability calculation problem for single-component systems is studied based on extreme shock model,cumulative shock model and δ shock model,respectively.On the one hand,the external shock may not only cause the system failure,but also increase the degradation level of the system,so as to accelerate the soft failure process.On the other hand,with the increase of system degradation,the system’s ability to withstand external shocks gradually decreases.That is,the hard failure threshold of the system changes with the degradation state of the system.Therefore,the interaction impact between soft and hard failures constitutes the mutually dependent competing failure processes.Under the three shock models and normal distribution,the reliability functions of products under the two failure mechanisms are calculated by using multivariate normal distribution theory.In addition,some important reliability indices of the system are calculated.Finally,numerical examples of the spool valve and reinforced concrete pile columns of sea bridge are given to verify the effectiveness of the proposed model.Secondly,under the assumptions that internal degradation has a linear degradation path and the arrival of external shocks follows the nonhomogeneous Poisson shock process,the reliability calculation problem for single-component systems is studied based on two kinds of generalized mixed shock models.In these models,the interdependence between soft failure and hard failure process is reflected as follows: 1)Each external shock brings an abrupt increment of the degradation to the system,thus accelerates the process of soft failure;2)The amount of system degradation influences the thresholds of the extreme shock and the δshock models.Therefore,the system is subject to mutually dependent and competing soft and hard failure processes.The first kind of generalized mixed shock model is a combination of a system-state dependent extreme shock model and a system-state dependent δshock model.When a single shock exceeds the hard failure threshold,or the arrival time between two consecutive shocks is less than the recovery time threshold,a hard failure occurs.The second kind of generalized mixed shock model is a combination of a system-state dependent cumulative shock model and a system-state dependent δshock model.When the accumulated shock magnitude exceeds the hard failure threshold,or the arrival time between two consecutive shocks is less than the recovery time threshold,a hard failure occurs.Under both the two kinds of generalized mixed shock models and normal distribution,the reliability functions and some reliability indices of the systems under the two failure mechanisms are calculated by using multivariate normal distribution theory.In addition,some special cases of the model are also discussed.Finally,numerical examples of spool valve and sea bridge stone pier corrosion are given to verify the validity of the proposed model.Finally,under the assumptions that internal degradation has a linear degradation path and the arrival of the external shocks follows the nonhomogeneous Poisson shock process,the reliability calculation problem for multi-component system is studied based on the extreme shock model and cumulative shock model,respectively.For these multi-component systems,on the one hand,the external shock will increase the degradation level of each component,so as to accelerate the process of its soft failure.On the other hand,external shocks also decrease the hard failure threshold of each component.Therefore,the soft and hard failures constitute mutually dependent competing failure processes.Under the two kinds of shock models normal distributions,the conditional survival probabilities of single components and any combination of multiple components are calculated by using multivariate normal distribution theory,and then the reliability functions of multi-component system under the two failure mechanisms are derived accordingly.In addition,some special cases of the k-out-of-n(G)system are discussed.Finally,numerical examples of a micro-engine are given to verify the effectiveness of the proposed model.