Non parametric estimation of reliability for parallel system under ranked set sampling

Xiaofang Dong, Xiangjia Fan and Liangyong Zhang

Communications in Statistics - Theory and Methods, 2025, vol. 54, issue 18, 5830-5849

Abstract: In order to improve the estimation efficiency of reliability for a two-component parallel system, this article presents a non parametric estimator of reliability based on ranked set sampling using the idea of U-statistics. The variance of the new estimator is calculated, and it is shown to be smaller than the variance of the corresponding non parametric estimator under simple random sampling. The new estimator is shown to have asymptotic normality, the asymptotic relative efficiency of the new estimator and the corresponding estimator under simple random sampling is analyzed, and the simulated relative efficiencies of small samples are calculated. The research results of estimation efficiencies show that the ranked set sampling method is always more efficient than the simple random sampling method. Finally, an empirical study based on real-life data supports the effectiveness of the proposed method.

Date: 2025
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DOI: 10.1080/03610926.2024.2447823

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