Statistical Analysis Of Two - Element Series System With Weibull Distribution

In the study of reliability of the system,A series systems is a basic system in the system re-liability assessment,It’s also common in the study of engineering problems,Due to the Weibulldistribution is based on the weakest link or series model,Can fully reflect the material source of de-fects and stress concentration on the influence of material fatigue life, And with increasing failurerate,So it is appropriate to use it as a life distribution model of material or fatigue strength underthe given life model,So it has important practical significance to carry out a statistical analysis onthe series of Weibull distribution system.This paper studies the statistical analysis of Weibull distribution in series system, Accordingto the distribution of the system,discusses the Images and properties of its density and failure ratefunction, And also some estimates of the scale and shape parameters,The main work of this articleare(1)Through cascading the two independented components whose life obeys Weibull distribu-tion,We give the definition of series life distribution Using the method of minimal value distribu-tion.(2)For density function and failure rate function of the distribution,IN two kinds of situations, Using the method of classification to discuss,discussing the monotonicity of the distribution,Andpresent function of images when the shape parameters take different values with Matlab soft-ware.(3)when m1is not equals m2, By using the convergence of infinite integral criteria,proves theexistence of the distribution K order origin moment, when m1equals m2,Using integral methodin huanyuan,Expressions are given for the K order origin moment.(4)Undering the whole sampledata,when m1is not equals m2, By putting the two components in series and seeking the like-lihood function respectively,Discusses the estimate of the Shape and scale parameters and provethe existence of the estimates. when m1equals m2,Discuss the moment estimation,maximumlikelihood estimates(MLE)and inverse moment estimates of the parameters,prove the existenceand uniqueness of the estimates,And when n take different vaules,through examples,calculate theparameter estimates by mathematical software Matlab.(5)Undering the destiny truncated sampledata, when m1equals m2, Discuss the maximum likelihood estimates and inverse moment esti-mates of the parameters, prove the existence and uniqueness of the estimates,And when n takedifferent vaules,through examples,calculate the parameter estimates by mathematical softwareMatlab,Meanwhile, lists the estimates under different values of r,Then finally present the life dataand calculation results,in the form of a table.