Optimality in Type I hybrid censoring with random sample size

This paper considers the Type I hybrid censoring and investigates the optimal value for the sample size which is assumed as a truncated binomial random variable‎. ‎Rayleigh distribution is considered for the lifetime distribution‎. ‎Towards this end‎, ‎various factors can be considered and the most important is the sampling cost criterion‎. ‎Since the sample size is a random variable‎, ‎the optimal parameter of the random sample size is determined so that the total cost of the test does not exceed a pre-determined value‎. ‎Numerical calculations and a simulation study have been performed to evaluate the obtained results‎. ‎Finally‎, ‎the conclusion of the article is presented.