On flexible progressive censoring

In life testing experiment under the setup of progressive Type II censoring we consider a new flexible scheme, in which the experimenter removes $r_1^{*}$ ( $r_1^{*}=r_1$ ) units from the experiment if the first failure occurs before some predefined time $t_1$ , and removes $r_1$ units when the first failure occurs after time $t_1$ . If the second failure occurs before the time $t_2$ , $r_2^{*}$ surviving items are removed at random, otherwise $r_2$ surviving units are removed, ( $r_2^{*}=r_2$ ), and so on; finally, after the $m$ th failure, all remaining items are removed. Under this setup of the experiment we study the distributions of failure times, which are entitled as flexible progressive Type II censored (FPC) order statistics. The simulation algorithm for generating FPC samples and an illustrative example for a special case of exponential distribution are also presented. Finally, a Monte Carlo study is also conducted for the expected termination time under FCP.