General Shock Moedel Based On Small Sample Data And Application

As one of the main research contents in the field of reliability,shock model is mainly used to describe the reliability change of the system when the system runs in an uncertain environment and is shocked by the outside world.In the equipment manufacturing industry,many systems will be affected by external shock during work,resulting in the gradual reduction of reliability.Therefore,it is of great significance to model and analyze the shock model.Traditional shock models are based on probability theory for modeling and analysis,while using probability theory to deal with problems requires three conditions: events need to be clearly defined;There are a large number of samples;There is probability repeatability between samples.However,there are few shock data available in the project,which does not meet the conditions of probability modeling.At this time,it is not suitable to use the probability method to model and analyze the reliability of the shock model.Experts are usually required to give the arrival time and intensity of the shock according to their own experience.Therefore,this paper models the general shock model based on uncertainty theory,and gives its reliability analysis.The main research contents are as follows:1.The reliability modeling and analysis method of shock model in the case of small samples are given.Assuming that the shock arrival time and shock strength are uncertain variables,the cumulative shock model and extreme shock model under uncertain environment are established,and the confidence reliability function of the system is obtained.It is analyzed that the reliability of the system decreases gradually with time.Finally,a numerical example is given to verify.2.The reliability modeling and evaluation method of shock model with change point in the case of small samples are given.The shock on the system changes suddenly due to the sudden change of the external environment.Therefore,the shock model with change point in uncertain environment is studied.Assuming that the time interval of shock arrival and shock strength are regarded as uncertain variables,and the shock strength increases significantly after the change point,the cumulative shock model and extreme shock model with change point under uncertain environment are established,and the reliability function of the system is given.Finally,a numerical example is given to verify.3.The reliability modeling and analysis method of mixed shock model in the case of small samples are given.Considering that the system is affected by both cumulative shock and extreme shock in real life,the mixed shock model in uncertain environment(the mixture of cumulative shock model and extreme shock model)is studied.Assuming that the time interval of shock arrival and shock strength are regarded as uncertain variables,and the cumulative shock strength and single shock strength will affect the reliability of the system,the mixed shock model under uncertain environment is established,and the reliability function of the system is given.Finally,a numerical example is given to verify.This research result provides a new idea for the reliability modeling and analysis method of shock model in the case of small samples,and has good practical value.