Statistical Analysis Based On The Composite Distribution Of BS Fatigue Life Distribution

In the reliability life research,product life test is usually carried out,and statistical characteristics of life test data are analyzed to reflect the law of product life.The failure of product is caused by many reasons.BS fatigue life distribution occurs because of cracks in products under certain periodic pressure.If the length of cracks reaches or exceeds a certain threshold,the products will fail.Because the density function of BS fatigue life distribution is very complex,it is difficult to estimate the parameters.So far,BS fatigue life distribution still has great theoretical significance and application value.In order to better study the life distribution of products,the academic community has emerged as the research direction of composite life distribution.The density function of the composite life distribution is more complex and can better fit the actual life data.The main work of this paper is based on the fatigue life distribution of BS,through the idea of composite distribution,the fatigue life distribution of BS is compounded with Poisson distribution,Binomial distribution and Geometric distribution respectively,thus a new life distribution is proposed,and some properties of its life distribution are studied.The distribution function,density function and failure rate function of BS—Poisson composite distribution,BS—Binomial composite distribution and BS—Geometric composite distribution are deduced theoretically;the image characteristics of their density function and failure rate function are investigated by drawing;the existence of k order moments is proved;the maximum likelihood estimation of parameters is deduced,and the approximate interval estimation of parameters under likelihood ratio method is given.For the approximate interval estimation of sample properties,the transcendental equations of parameters in maximum likelihood estimation are solved by fsolve statements in the Python library scipy.Optimize.Finally,a Monte-Carlo simulation example is given to calculate the maximum likelihood estimation and approximate interval estimation.Combining with the actual case,through the Kolmogorov test,the application value of the distribution is illustrated.