Nowadays, the use of various censorship methods has become widespread in industrial and clinical tests. Type I and Type II progressive censoring are two types of these censors. The use of these censors also has some disadvantages. This article tries to reduce the defects of the type I progressive censoring by making some change to progressive censorship. Considering the number and the time of the withdrawals as a random variable, this is done. First, Type I, Type II progressive censoring and two of their generalizations are introduced. Then, we introduce the new censoring based on the Type I progressive censoring and its probability density function. Also, some of its special cases will be explained and a few related theorems are brought. Finally, the simulation algorithm is brought and for comparison of introduced censorship against the traditional censorships a simulation study was done.

In this paper, a general method for goodness of fit test for the location-scale family of distributions under Type-II progressive censoring is presented and its properties are investigated. Then, using Monte Carlo simulation studies, the power of this test is compared with the powers of some existing tests for testing the Gumbel distribution. Finally the proposed test is used for fitting a distribution to a real data set.