In the Weibull process, the peril rate is zero or infinite when time equals zero. In order to solve this problem of fitting in the engineering, the position element was put forward to revise the Weibull process. Iterative fitting, correlation coefficients method and maximum likelihood method were integrated to obtain the estimations of the scale, shape and position elements in the Weibull process. And meanwhile, some relative reliable characteristics were also estimated. An application example shows the estimations of these parameters can satisfied the requirements by using of this method, when repairable system is fitted by three-parameter Weibull process in the engineering.