Optimal random sample size in progressively type-II censoring based on cost constraint for the proportional hazards family. (English) Zbl 07497098
Summary: Perhaps the most frequently asked question concerning sampling is, ‘What sample size do we need?’. The answer to this question is influenced by many factors. Here, we consider the progressively type II censoring and respond to this question by considering the cost of experiment for the proportional hazard rate models. Towards this end, we first introduce a cost function and then by minimizing it we discuss the problem of finding optimal sample size. It is assumed that the sample size is a random variable. Some known candidates for the random sample size, namely the degenerate, binomial, and Poisson distributions, are considered and then we find the parameter of them such that the cost of experiment is bounded. To show the usefulness of results, one special case of the PHR model, the one-parameter Rayleigh distribution is considered. Then, numerical computations and simulation studies are reported. Finally, some concluding remarks are presented.
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