Nonparametric Estimation of System Reliability Under Ranked Set Sampling

DONG Xiaofang, ZHANG Liangyong

Journal of Systems Science and Mathematical Sciences ›› 2023, Vol. 43 ›› Issue (6) : 1635-1646.

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Journal of Systems Science and Mathematical Sciences ›› 2023, Vol. 43 ›› Issue (6) : 1635-1646. DOI: 10.12341/jssms22503

Nonparametric Estimation of System Reliability Under Ranked Set Sampling

  • DONG Xiaofang, ZHANG Liangyong
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Abstract

For the nonparametric estimation problem of the stress-strength system reliability, this paper presents the two sample U-statistics of system reliability using ranked set sampling method. The new estimator is shown to have asymptotic normality, and its asymptotic variance is given. The asymptotic relative efficiencies of the new statistics and the corresponding U-statistics under simple random sampling are analyzed, and the simulated relative efficiencies of small samples are calculated. The research results of asymptotic relative efficiencies and simulated relative efficiencies show that the two sample U-statistics under ranked set sampling is always more efficient than the corresponding U-statistics under simple random sampling. Finally, the actual analysis results of strength data of single carbon fibers verify the high efficiency of ranked set sampling method.

Key words

Ranked set sampling / system reliability / U-statistics / asymptotic relative efficiency

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DONG Xiaofang , ZHANG Liangyong. Nonparametric Estimation of System Reliability Under Ranked Set Sampling. Journal of System Science and Mathematical Science Chinese Series, 2023, 43(6): 1635-1646 https://doi.org/10.12341/jssms22503

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