The Properties Of 2 χ~2 Renewal Process And Geometric Process

Renewal process is a counting process that the point distance is independent and identically distributed, and it is a random process reaches relative earlier, it mainly originated the replacement problems and machine maintenance problems. When the point distance is independent and all isχ~2 distribution, which is known as Poisson process. But in practice, sometimes the point distance is independent but all obeysχ~2 distribution, this is what reached in this paper-χ~2 renewal process.Renewal process in practical application are still have some restrictions, such as mechanical maintenance problems, renewal process hypothesis machine maintain the same distribution after maintenance with the original parts have, and the actual situation is the life of the machine is shorter and shorter, he will finally be unable to work. In order to solve this problem, Lin YE promote the renewal process, when its point distance independent but not necessarily with the same distribution, defines a new process - the geometric process. Geometric process is more general and have more application than renewal process.From the above we know,χ~2 renewal process is a special situation of the renewing process, geometric process is the promotion of renewing process. This paper mainly discuss the properties ofχ~2 renewal process and geometric process, gives a renewal functionχ~2renewal process , and illustrates its application in the field of transportation; describes the study of the geometric process and the residual life, age distribution and the joint distribution. Due to the renewal process is a exceptions of geometric process, this paper take special value, and verifies the correctness of the results .The part of the results have been published in paper [2], [3] .