Reliability Analysis Of Shock Model Under Uncertain Environment

The shock model is an important part of the reliability theory and is generally used to model the survival,failure and maintenance of systems in non-deterministic environments.However,in the process of studying the shock model,we have to face all kinds of non-deterministic factors,including the phenomenon of randomness,uncertainty and the coexistence of randomness and uncertainty.Although probability theory is an effective mathematical tool to study this non-determinism.Using probability theory to deal with engineering problems depends on three premises:the clearly defined event,a large number of samples and probability of repeatability among the samples.When the above conditions are not met at the same time,the probability theory cannot be used.When no samples are available to estimate a probability distribution,we usually invite some domain experts to evaluate the belief degree that each event will happen.The uncertainty theory is the mathematical branch used to deal with subjective reliability.Therefore,in this paper,the shock model is modeled and analyzed separately for uncertain situations and uncertain and random coexistence situations,mainly doing the following research:When the shock model does not have a large number of samples,the shock model is modeled and analyzed by using uncertainty theory.Assume that the system is composed of two components and it has three independent shock sources.We also assume that the shock sources leading to failure for components and the failure times are uncertain.Based on that,the fatal shock model is established and analyzed.Furthermore,the joint survival uncertainty distribution for the lifetimes of the two components and some basic theorems are arrived,respectively.Finally,some numerical examples are given.In actual fatal shock models analysis,there has both random and uncertain factors.Under uncertain random environment,it is assumed that the system is composed of two components and has six independent shock sources.There are two major types of shock sources in this system,one type of shock source is supported by statistical data,and the other one is supported by expert experience.The chance theory is introduced into the study of the fatal shock models.Based on that,the fatal shock model under uncertain random environment is established.The joint survival chance distribution for the lifetimes of the two components and some basic theorems are presented.Finally,some numerical examples are given.The paper provides a new modeling method for the development of reliability mathematics and related fields.It not only has academic significance,but also has practical value and broad application prospects.