Statistical Analysis Of Two-parameter Flexible Weibull Distribution And Lomax Distribution

This paper is divided into two parts.In the first part,the analysis of reliability statistics of two-parameter flexible Weibull dis-tributions is studied.The features of the density function and mean failure rate function are strictly proved.The following conclusions are obtained:(1)The density function of the two-parameter flexible Weibull distribution has a 'one-peak' shape;(2)The feature of the mean failure rate function is divided into two cases:(i)When(?)?1/2,it increases monotonous-ly;(ii)When 0<(?)<1/2 it takes the form of 'N'.In addition,the existence of the k-order moment of the distribution is also proved.Three kinds of parameter estimations are provid-ed:regression estimation,inverse moment estimation and maximum likelihood estimation,as well as approximate interval estimation.The Monte-Carlo simulation method is used to compare the performance of the three point estimations under different conditions.Finally,we obtain the data which obeys the two-parameter flexible Weibull distribution by the fitting test method for the example of the reaction pump,and the point estimation and approximate interval estimation of the parameters of the example are also derived.In addition,part of the experimental data is simulated,the parameter point estimation and approximate interval estimation based on this data are given.The second part mainly studies the statistical analysis of Lomax distribution under differ-ent loss models and different accelerated life tests.First,for the cumulative exposure model:(1)We study the failure mode and the maximum likelihood estimation of Lomax distribution under the step-by-step stress accelerated life test.(2)We discuss the failure mode and max-imum likelihood estimation under multiple sets of stress accelerated life tests:(3)We study the failure mode and maximum likelihood estimation under a progressive-constant stress ac-celerated life test;(4)We discuss the failure mode and maximum likelihood estimation under the cycled progressive stress accelerated life test.Afterwards,for the tampered failure rate model:We study the failure mode and maximum likelihood estimation under sample steps stress accelerated life test in the case of full simples and in the case of censored numbers,respectively.