Unbiased estimation of P( X > Y )using ranked set sample data
TL;DR: In this article, the problem of unbiased estimation of P[X>Y] using ranked set sample data for two independent random variables X and Y with unknown probability distributions was considered, and it was proved that the ranked set samples provided an unbiased estimator with smaller variance as compared with simple random samples of same sizes.
Abstract: The problem considered is that of an unbiased estimation of P[X>Y] using ranked set sample data for two independent random variables X and Y with unknown probability distributions. Postulating a model for imperfect ranking, it is proved that the ranked set samples provide an unbiased estimator with smaller variance as compared with simple random samples of same sizes, even when the rankings are imperfect. It is further shown that the ranked set sampling provides maximum efficiency when the rankings are perfect.
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TL;DR: In this paper, survival distributions for reliability applications in the Biomedical Sciences are discussed, with a focus on the reliability of the distribution of survival distributions in the field of bio-medical applications.
Abstract: (1976). Survival Distributions: Reliability Applications in the Biomedical Sciences. Technometrics: Vol. 18, No. 4, pp. 501-501.
513 citations
TL;DR: An introduction to the basic concepts underlying ranked set sampling, in general, with specific illustrations from the one- and two-sample settings are provided and targeted discussion of the many options available to the researcher within the RSS paradigm is discussed.
Abstract: Ranked set sampling (RSS) is an approach to data collection and analysis that continues to stimulate substantial methodological research. It has spawned a number of related methodologies that are active research arenas as well, and it is finally beginning to find its way into significant applications beyond its initial agricultural-based birth in the seminal paper by McIntyre (1952). In this paper, we provide an introduction to the basic concepts underlying ranked set sampling, in general, with specific illustrations from the one- and two-sample settings. Emphasis is on the breadth of the ranked set sampling approach, with targeted discussion of the many options available to the researcher within the RSS paradigm. The paper also provides a thorough bibliography of the current state of the field and introduces the reader to some of the most promising new methodological extensions of the RSS approach to statistical data analysis.
109 citations
TL;DR: In this article, the authors obtained the estimators of R based on RSS using maximum likelihood (ML) and modified maximum likelihood(MML) methodologies and compared them with their counterparts based on simple random sampling (SRS) using Monte Carlo simulation.
Abstract: This paper deals with making inferences regarding system reliability when the distribution of the stress X and the strength Y are independent Weibull. In the literature, estimators based on simple random sampling (SRS) are widely used in estimating R. However, in recent years, ranked set sampling (RSS) has become popular in performing statistical inference. We, therefore, obtain the estimators of R based on RSS using maximum likelihood (ML) and modified maximum likelihood (MML) methodologies. The performances of the proposed estimators are compared with their counterparts based on SRS using Monte Carlo simulation. The simulation results show that the proposed estimators are more preferable than the estimators based on SRS in terms of efficiency. In addition, under the assumption of imperfect ranking the efficiencies of the ML and the MML estimators of R, based on RSS, are compared and the ML estimator of R is found to be more efficient. Finally, a real data-set is analysed to demonstrate the imple...
36 citations
Cites background or methods from "Unbiased estimation of P( X > Y )us..."
...However, iterative methods can be problematic because of the following reasons: (i) convergence to wrong roots, (ii) convergence to multiple roots, and (iii) non-convergence of iterations, see, for example, Smith (1985); Puthenpura and Sinha (1986) and Vaughan (2002)....
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...In the context of estimation of R, Sengupta and Mukhuti (2008a, 2008b), Muttlak et al. (2010) and Dong et al. (2013) derived the estimator of the system reliability R using RSS data....
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TL;DR: In this paper, the authors considered point and interval estimation of stress-strength reliability based on ranked set sampling when the distribution of the stress and the strength are both Lindley and showed that the reliability of the reliability depends on the rank set sampling.
Abstract: In this study, we consider point and interval estimation of stress–strength reliability R=P(X
31 citations
01 Sep 2018
TL;DR: In this article, a dynamic reliability measure based on ranked set sampling is introduced, and its properties are investigated in theory and simulation, and the results support the preference of the suggested index over the analogous one in simple random sampling.
Abstract: In this article, a dynamic reliability measure based on ranked set sampling is introduced, and its properties are investigated in theory and simulation. The results support the preference of the suggested index over the analogous one in simple random sampling. A data set from an agricultural experiment is analyzed for illustration.
25 citations
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TL;DR: The application of the ranked sample method to pasture measurement is discussed and the means of such a sample is slightly less than (n + 1)/2 times more efficient than the mean of n items taken at random.
Abstract: A new method of sampling is described Take the largest in the first of n sets, each of n random items, the second largest in the second set, and so on to the smallest in the nth set The sample of n items selected in this way is an unbiased sample of the population For typical unimodal distributions the mean of such a sample is slightly less than (n + 1)/2 times more efficient than the mean of n items taken at random The application of the ranked sample method to pasture measurement is discussed
1,158 citations
Book•
01 Jan 1975
535 citations
TL;DR: In this paper, survival distributions for reliability applications in the Biomedical Sciences are discussed, with a focus on the reliability of the distribution of survival distributions in the field of bio-medical applications.
Abstract: (1976). Survival Distributions: Reliability Applications in the Biomedical Sciences. Technometrics: Vol. 18, No. 4, pp. 501-501.
513 citations
Book•
01 Mar 2003
TL;DR: A survey of applications theory and general estimation procedures for stress strength models can be found in this paper, along with examples and details on applications and their application in the context of point estimation and statistical inference.
Abstract: Stress-strength models - history, mathematical tools and survey of applications theory and general estimation procedures parametric point estimation parametric statistical inference nonparametric methods special cases and generalizations examples and details on applications
387 citations