optimization problem in type ii hybrid censoring with fixed and random sample size

In this paper‎, ‎we study type ii hybrid censoring and the related problem of finding the optimal sample size‎. ‎the rayleigh distribution is considered for the lifetime distribution‎. ‎additionally‎, ‎the sample size is assumed to be either a fixed value or a random variable drawn from a geometric distribution‎. ‎one of the most important criteria for studying this problem is the cost associated with the experiment‎. ‎therefore‎, ‎the optimal sample size is determined such that the cost function does not exceed a pre-defined value‎. ‎in the case where the sample size is a random variable‎, ‎the goal is to identify the optimal parameters for the distribution‎. ‎to evaluate the obtained results‎, ‎numerical computation‎, ‎a simulation study‎, ‎and a real example have been performed‎. ‎finally‎, ‎the conclusions of the article are presented.