Renewal Function Approximation Method Of Weibull Distribution Research Distribution

Random process provides a theoretical basis for the modeling of various uncertain behaviors in social daily life and industrial production.Due to its characteristics and the principle of various reliability,maintenance,performance optimization and other related problems existing in engineering production and operation,the renewal process of random process was applied to the replacement of mechanical parts in the earliest research,similar to the minimum maintenance optimization of equipment.However,the renewal process is still subject to some theoretical and technical limitations in practical application,such as the maintenance of the machine.When dealing with the problem,the renewal process requires the distribution of the original parts,which should be consistent with the remaining life of the machine after maintenance.Renewal function is a complex mathematical model in essence as the cornerstone of the analy sis of renewal process.It is of great significance to study and analyze the algorithm,approximation and application of renewal function in order to expand its application field and break the bottleneck of theoretical application.The specific research contents are as follows:(1)By analyzing the calculation methods of the renewal function of the existing typical distribution function,it is found that the idea of numerical calculation is very similar,which is calculated in the form of integral definition.However,due to the diversity of derivation methods,the degree of difficulty of calculation is also different.(2)By comparing the accuracy of the renewal function approximation method,it is concluded that the closed form expression is obviously better than the traditional numerical calculation for the reliability problem,and a simple renewal function calculation method is proposed,which can be used to solve the renewal function of various probability densities,and the accuracy of this method is quite high.(3)Based on the above theory and analysis,a new renewal function approximation method is developed;The approximate error of renewal function of weibull distribution is improved obviously.(4)The application of renewal function in queuing theory,production and spare parts control,quality assurance decision,reliability and maintenance decision optimization is systematically analyzed,and the important position of renewal function in practical application is further explained,and the accuracy of the new method is verified by relevant cases.