Statistical Inference of Stress-Strength Reliability for Burr Distributions Based on Ranked Set Sampling

A fundamental issue in several studies is the need for cost-effective sampling, particularly when measuring a significant characteristic is expensive, uncomfortable, or time-consuming. In terms of precision achieved per unit of sample, the ranked set sampling (RSS) approach offers a practical way to achieve observational economy. In the current work, ten frequentist estimation strategies are considered for the reliability of the stress strength parameter λ=P[T<Z], where T and Z are independent random variables following the Burr III and Burr XII distributions, respectively, that share the same shape parameter. Percentiles and weighted least squares, Anderson-Darling, maximum likelihood, minimum spacing absolute log distance, least squares, Cram’er-von Mises, maximum product of spacing, right-tailed Anderson-Darling, and minimum spacing absolute distance are some recommended estimation methods for the RSS and simple random sample methods. The effectiveness of the proposed RSS-based approximations is evaluated using simulation work employing certain accuracy standards. We conclude that the maximum product spacing and percentile approaches are the lowest in the mean squared error values for the reliability estimate when compared to those of the other alternatives. Two real data sets that trade share data and the prices of the 31 distinct children’s wooden toys are used to provide further findings.