Concomitant record ranked set sampling

In this work, we define a new method of ranked set sampling (RSS) which is suitable when the characteristic (variable) Y of primary interest on the units is jointly distributed with an auxiliary characteristic X on which one can take its measurement on any number of units, so that units having record values on X alone are ranked and retained for making measurement on Y. We name this RSS as concomitant record ranked set sampling (CRRSS). We propose estimators of the parameters associated with the variable Y of primary interest based on observations of the proposed CRRSS which are applicable to a very large class of distributions viz. Morgenstern family of distributions. We illustrate the application of CRRSS and our estimation technique of parameters, when the basic distribution is Morgenstern-type bivariate logistic distribution. A primary data collected by CRRSS method is demonstrated and the obtained data used to illustrate the results developed in this work.     

Mixed ranked set sampling design

The main focus of agricultural, ecological and environmental studies is to develop well designed, cost-effective and efficient sampling designs. Ranked set sampling (RSS) is one method that leads to accomplish such objectives by incorporating expert knowledge to its advantage. In this paper, we propose an efficient sampling scheme, named mixed RSS (MxRSS), for estimation of the population mean and median. The MxRSS scheme is a suitable mixture of both simple random sampling (SRS) and RSS schemes. The MxRSS scheme provides an unbiased estimator of the population mean, and its variance is always less than the variance of sample mean based on SRS. For both symmetric and asymmetric populations, the mean and median estimators based on SRS, partial RSS (PRSS) and MxRSS schemes are compared. It turns out that the mean and median estimates under MxRSS scheme are more precise than those based on SRS scheme. Moreover, when estimating the mean of symmetric and some asymmetric populations, the mean estimates under MxRSS scheme are found to be more efficient than the mean estimates with PRSS scheme. An application to real data is also provided to illustrate the implementation of the proposed sampling scheme.     

Robust extreme ranked set sampling

In this paper, a robust extreme ranked set sampling (RERSS) procedure for estimating the population mean is introduced. It is shown that the proposed method gives an unbiased estimator with smaller variance, provided the underlying distribution is symmetric. However, for asymmetric distributions a weighted mean is given, where the optimal weights are computed by using Shannon's entropy. The performance of the population mean estimator is discussed along with its properties. Monte Carlo simulations are used to demonstrate the performance of the RERSS estimator relative to the simple random sample (SRS), ranked set sampling (RSS) and extreme ranked set sampling (ERSS) estimators. The results indicate that the proposed estimator is more efficient than the estimators based on the traditional sampling methods.     

Stratified pair ranked set sampling

Stratified pair ranked set sampling is introduced and applied in estimating the population mean. Mathematical properties of the suggested estimator are treated. The estimator and its competitors are also compared through some numerical studies. Usefulness of the proposed design is illustrated using a cost analysis.     

The mg-procedure in ranked set sampling

The MG-procedure in ranked set sampling is studied in this paper. It is shown that the MG-procedure with any selective probability matrix provides a more efficient estimator than the sample mean based on simple random sampling. The optimum selective probability matrix in the procedure is obtained and the estimator based on it is shown to be more efficient than that studied by Yanagawa and Shirahata [5]. The median-mean estimator, which is more efficient and could be easier to apply than that proposed by McIntyre [2] and Takahashi and Wakinoto [3], is proposed when the underlying distribution function belongs to a certain subfamily of symmetric distribution functions which includes the normal, logistic and double exponential distributions among others.     

Robust extreme double ranked set sampling

As a well-known method for selecting representative samples of populations, ranked set sampling (RSS) has been considered increasingly in recent years. This (RSS) method has proved to be more efficient than the usual simple random sampling (SRS) for estimating most of the population parameters. In order to have a more efficient estimate of the population mean, a new sampling scheme called as robust extreme double ranked set sampling (REDRSS) is introduced and investigated in this paper. A simulation study shows that using REDRSS scheme gives more efficient estimates of population mean with smaller variance than the usual SRS, RSS and most other sampling schemes based on RSS estimators in non-uniform (symmetric or non-symmetric) distributions.     

Stein-type estimation using ranked set sampling

In this study, we consider the application of the James–Stein estimator for population means from a class of arbitrary populations based on ranked set sample (RSS). We consider a basis for optimally combining sample information from several data sources. We succinctly develop the asymptotic theory of simultaneous estimation of several means for differing replications based on the well-defined shrinkage principle. We showcase that a shrinkage-type estimator will have, under quadratic loss, a substantial risk reduction relative to the classical estimator based on simple random sample and RSS. Asymptotic distributional quadratic biases and risks of the shrinkage estimators are derived and compared with those of the classical estimator. A simulation study is used to support the asymptotic result. An over-riding theme of this study is that the shrinkage estimation method provides a powerful extension of its traditional counterpart for non-normal populations. Finally, we will use a real data set to illustrate the computation of the proposed estimators.     

Reliability estimation based on ranked set sampling

In this paper we consider the problem of estimating the reliability of an exponential component based on a Ranked Set Sample (RSS) of size n. Given the first r observations of that sample, 1≤r≤n, we construct an unbiased estimator for this reliability and we show that these n unbiased estimators are the only ones in a certain class of estimators. The variances of some of these estimators are compared. By viewing the observations of the RSS of size n as the lifetimes of n independent k-out-of-n systems, 1≤k≤n, we are able to utilize known properties of these systems in conjunction with the powerful tools of majorization and Schur functions to derive our results.     

On extropy properties of ranked set sampling

Ranked set sampling is a sampling design that allows the experimenter to span the full range values in the population and it can be used widely in industrial, environmental and ecological studies. In this paper, we consider the information content of ranked set sampling in terms of extropy measure. It is shown that the ranked set sampling performs better than its simple random sample counterpart of the same size. Monotone properties and stochastic orders are investigated. Sharp bounds on the extropy of RSS data based on the projection method in the non-parametric set-up as well as Steffensen inequalities in the parametric context are established. The extropy measure can also be used as a discrimination tool between RSS and SRS data.     

Steady-state ranked set sampling and parametric estimation

Ranked set sampling (RSS) was first used to obtain a more efficient estimator of the population mean, as compared to the one based on simple random sampling. This technique is useful when judgment ordering of a simple random sample (SRS) of small size can be done easily and fairly accurately, but exact measurement of an observation is difficult and expensive. It is noted that, due to the complicated likelihood, parametric estimation with RSS is difficult. In this article, the notion of steady-state RSS is introduced, its relation to stratified sampling is established, and its possible use in parametric estimation is explored and put forward for further investigations.     

New two-stage sampling designs based on neoteric ranked set sampling

Neoteric ranked set sampling (NRSS) is a recently developed sampling plan, derived from the well-known ranked set sampling (RSS) scheme. It has already been proved that NRSS provides more efficient estimators for population mean and variance compared to RSS and other sampling designs based on ranked sets. In this work, we propose and evaluate the performance of some two-stage sampling designs based on NRSS. Five different sampling schemes are proposed. Through an extensive Monte Carlo simulation study, we verified that all proposed sampling designs outperform RSS, NRSS, and the original double RSS design, producing estimators for the population mean with a lower mean square error. Furthermore, as with NRSS, two-stage NRSS estimators present some bias for asymmetric distributions. We complement the study with a discussion on the relative performance of the proposed estimators. Moreover, an additional simulation based on data of the diameter and height of pine trees is presented.     

Statistical quality control based on ranked set sampling

Different quality control charts for the sample mean are developed using ranked set sampling (RSS), and two of its modifications, namely median ranked set sampling (MRSS) and extreme ranked set sampling (ERSS). These new charts are compared to the usual control charts based on simple random sampling (SRS) data. The charts based on RSS or one of its modifications are shown to have smaller average run length (ARL) than the classical chart when there is a sustained shift in the process mean. The MRSS and ERSS methods are compared with RSS and SRS data, it turns out that MRSS dominates all other methods in terms of the out-of-control ARL performance. Real data are collected using the RSS, MRSS, and ERSS in cases of perfect and imperfect ranking. These data sets are used to construct the corresponding control charts. These charts are compared to usual SRS chart. Throughout this study we are assuming that the underlying distribution is normal. A check of the normality for our example data set indicated that the normality assumption is reasonable.     

Estimation of bivariate characteristics using ranked set sampling

The superiority of ranked set sampling (RSS) over simple random sampling (SRS) for estimating the mean of a population is well known. This paper introduces and investigates a bivariate version of RSS for estimating the means of two characteristics simultaneously. It turns out that this technique is always superior to SRS and the usual univariate RSS of the same size. The performance of this procedure for a specific distribution can be evaluated using simulation or numerical computation. For the bivariate normal distribution, the efficiency of the procedure with respect to that of SRS is evaluated exactly for set size m = 2 and 3. The paper shows that the proposed estimator is more efficient than the regression RSS estimators proposed by Yu & Lam (1997) and Chen (2001). Real data that consist of heights and diameters of 399 trees are used to illustrate the procedure. The procedure can be generalized to the case of multiple characteristics.     

Partial groups ranked set sampling and mean estimation

Ranked set sampling (RSS) is an advanced sampling method which is very effective for estimating mean of the population when exact measurement of observation is difficult and/or expensive. Balanced Groups RSS (BGRSS) is one of the modification of RSS where only the lowest, the median and the largest ranked units are taken into account. Although BGRSS is advantageous and useful for some specific cases, it has strict restrictions regarding the set size which could be problematic for sampling plans. In this study, we make an improvement on BGRSS and propose a new design called Partial Groups RSS which offers a more flexible sampling plan providing the independence of the set size and sample size. Partial Groups RSS also has a cost advantage over BGRSS. We construct a Monte Carlo simulation study comparing the performance of the mean estimators of the proposed sampling design and BGRSS according to their sampling costs and mean squared errors for various type of distributions. In addition, we give a biometric data application for investigating the efficiency of Partial Groups RSS in real life applications.     

An extension of the ranked set sampling theory

This paper is concerned with ranked set sampling theory which is useful to estimate the population mean when the order of a sample of small size can be found without measurements or with rough methods. Consider n sets of elements each set having size m. All elements of each set are ranked but only one is selected and quantified. The average of the quantified elements is adopted as the estimator. In this paper we introduce the notion of selective probability which is a generalization of a notion from Yanagawa and Shirahata (1976). Uniformly optimal unbiased procedures are found for some (n,m). Furthermore, procedures which are unbiased for all distributions and are good for symmetric distributions are studied for (n,m) which do not allow uniformly optimal unbiased procedures.     

Estimating variances of strata in ranked set sampling

In RSS, the variance of observations in each ranked set plays an important role in finding an optimal design for unbalanced RSS and in inferring the population mean. The empirical estimator (i.e., the sample variance in a given ranked set) is most commonly used for estimating the variance in the literature. However, the empirical estimator does not use the information in the entire data over different ranked sets. Further, it is highly variable when the sample size is not large enough, as is typical in RSS applications. In this paper, we propose a plug-in estimator for the variance of each set, which is more efficient than the empirical one. The estimator uses a result in order statistics which characterizes the cumulative distribution function (CDF) of the rth order statistics as a function of the population CDF. We analytically prove the asymptotic normality of the proposed estimator. We further apply it to estimate the standard error of the RSS mean estimator. Both our simulation and empirical study show that our estimators consistently outperform existing methods.     

New imperfect rankings models for ranked set sampling

Ranked set sampling is a sampling approach that leads to improved statistical inference in situations where the units to be sampled can be ranked relative to each other prior to formal measurement. This ranking may be done either by subjective judgment or according to an auxiliary variable, and it need not be completely accurate. In fact, results in the literature have shown that no matter how poor the quality of the ranking, procedures based on ranked set sampling tend to be at least as efficient as procedures based on simple random sampling. However, efforts to quantify the gains in efficiency for ranked set sampling procedures have been hampered by a shortage of available models for imperfect rankings. In this paper, we introduce a new class of models for imperfect rankings, and we provide a rigorous proof that essentially any reasonable model for imperfect rankings is a limit of models in this class. We then describe a specific, easily applied method for selecting an appropriate imperfect rankings model from the class.     

Lifetime performance index based on ranked set sampling

In this article, we assume that the lifetimes of products follow a one-parameter exponential distribution and use both conjugate and Jeffreys prior distributions for finding a Bayes estimator based on the RSS scheme for lifetime performance index CL. We also obtained maximum likelihood and adhac estimators for CL. Monte Carlo simulation study is done for comparing the obtained estimators in two sampling schemes SRS and RSS. Fisher information has been utilized to obtain lower confidence bound of CL for both schemes in asymptotically state and use this bounds for hypothesis testing of CL.     

Shrinkage estimation in replicated median ranked set sampling

In this article, we consider the median ranked set sampling estimation and test of hypothesis for the mean for symmetric distributions. We suggest some alternative estimation strategies for parameters based on shrinkage and pretest principles. It is advantageous to use the non-sample information in the estimation process to construct alternative estimations for the parameter of interest. In this article, large sample properties of the suggested estimators will be assessed numerically using computer simulation. The relative performance of the suggested estimators for moderate and large samples will also be simulated. For illustration purposes, the proposed methodology is applied using data collocated from the Pepsi Cola production company in Al-Khobar, Saudi Arabia.