A Further Study on Reliable Life Estimation under Ranked Set Sampling

Abstract

This article considers nonparametric estimation of reliable life based on ranked set sampling and its properties. It is proven analytically that the large sample efficiency of the reliable life estimator under the balanced ranked set sampling is higher than that under the simple random sampling of the same size, but the relative efficiency damps away as the reliable life moves away from the median on both directions. To improve the efficiency for the estimation of extreme reliable life, we then propose a reliable life estimator under a modified ranked set sampling protocol, its strong consistency and asymptotic normality are established. The proposed sampling is shown to be superior to the balanced ranked set sampling, and the relative advantage improves as the reliable life moves away from median. Finally, results of simulation studies for small sample as well as an application to a real data set are presented to illustrate some of the theoretical findings.

Keywords:

• Asymptotic normality
• Efficiency
• Ranked set sampling
• Reliable life
• Strong consistency

Mathematics Subject Classification:

• Primary 62N02
• Secondary 62G05, 62G30

Acknowledgments

The authors would like to thank the referees for their valuable comments that improved the presentation of this article. This work was supported by the Youth Teachers’ Scientific Research Start-up Assistance Program of Qiqihar University (2010 K-M28).

This work is an extension of the article that appeared in the Proceedings of MMR 2011.

Notes

Note. MSE1 = simulated mean square error for .

MSE2 = simulated mean square error for .

MSE3 = simulated mean square error for .

BIAS1 = simulated bias for .

BIAS2 = simulated bias for .

BIAS3 = simulated bias for .

Please see note for Table 3