Smooth estimation of a reliability function in ranked set sampling

ABSTRACT

The authors develop a kernel-based estimator of a dynamic reliability measure for use with independent ranked set samples. The estimator is in the form of a ratio, whose numerator and denominator are shown to outperform their rivals based on simple random samples. Some asymptotic properties about the proposed estimator are also established. Simulation studies reveal finite-sample properties of the estimator. The technique is finally applied on an agricultural data set.

KEYWORDS:

• Bandwidth selection
• judgment ranking
• stress-strength model

MSC2010:

• 62G30
• 62N05

Acknowledgments

Comments and suggestions by two anonymous reviewers as well as the Associate Editor were gratefully received.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

M. Mahdizadeh http://orcid.org/0000-0002-2355-9259

Ehsan Zamanzade http://orcid.org/0000-0002-6176-0607

Additional information

Funding

E. Zamanzade's research was carried out in Institute for Research in Fundamental Sciences (IPM) Isfahan branch and was in part supported by a grant from IPM [grant number 96620062].

Notes on contributors

M. Mahdizadeh

M. Mahdizadeh received his Ph.D. in Statistics from Ferdowsi University of Mashhad in 2011. Since then, he has taught Statistics at Hakim Sabzevari University. His research interests include ordered data, Monte Carlo methods, and goodness-of-fit tests.

Ehsan Zamanzade

Ehsan Zamanzade got his Ph.D. in Statistics from Ferdowsi University of Mashhad in 2012. He is an Associate Professor at the University of Isfahan. His main research interests include ranked set sampling, goodness-of-fit tests and entropy estimation.