Fluctuation Analysis Of The Instantaneous Availability For A One-unit Repairable System

Theoretical analysis of instantaneous availability is made for a one-unit repairable system in this thesis.Because the running state of a system or component has fluctuation in the initial stage,it is important to research its mechanism.This thesis researches this problem by the model with two states(up and repair)and that with three states(up,delay-repair and repair).Firstly,describing the phenomenon,this thesis puts forward a set of fluctuation theory including fluctuation definition,decision lemmas and initial amplitude.On a basis of this theory,the thesis decides the fluctuation of instantaneous availability.Secondly,based on renewal models,the thesis transforms the renewal equation into an ordinary differential equation to solve its analytical expression.By the fluctuation theory,the fluctuation of instantaneous availability is decided.The instantaneous availability has no fluctuation for the two-state model based on exponential distributions;however,it has fluctuation for the model based on uniform distributions or the combination of uniform and exponential distribution.Further,the fluctuation of instantaneous availability is conditional for the three-state model based on exponential distributions.Thirdly,the thesis researches the problem of fluctuation suppression by using different methods.Reasonable explanation makes methods to suppress fluctuation feasible.For the two-state model,the thesis uses parameters optimization to reduce initial amplitude,which makes fluctuation suppress;for the three-state model,by making the sensitivity analysis,the thesis shows the influence of parameters on the fluctuation of instantaneous availability.For certain conditions,the maintenance policy to substitute minor-repair for delay-repair is used.The new model has a simpler fluctuation condition and the higher steady-state availability.Finally,methods above are difficult to apply in the general situation.The approximation of instantaneous availability can be obtained by using two numerical integrations for the renewal equation.The error can be controlled in theory,which ensures the correctness of fluctuation decision.