Ranked Set Sampling Research Articles

A Distribution-Free THWMA Control Chart under Ranked Set Sampling

The basic assumption of the parametric control charts is that the underlying process follows the specific distribution. The appropriateness of parametric control charts is questionable when different industrial applications do not support this desired assumption. Recently, nonparametric control charts have been introduced to overcome this deficiency of parametric control charts. Nonparametric control charts have the same in-control run-length characteristics for all continuous distributions and are in-control robust. On the other hand, the ranked set sampling technique is preferred over the simple random sampling technique with control charts because it reduces variability and improves the control chart’s performance. So, this study aims to propose a nonparametric triple homogenously weighted moving average control chart under Wilcoxon signed-rank test with a ranked set sampling technique (regarded as NPTHWMA RSS ) to further enhance the process location monitoring. Monte Carlo simulations are used for computational purposes. The proposed control chart’s run-length performance is compared with competing control charts, like TEWMA-SR, TEWMA- X ¯ , TEWMA-SN, TEWMA- SR RSS , and NPDHWMA RSS control charts. The comparison revealed that the proposed NPTHWMA RSS control chart outperformed the other competing control charts, particularly for small to moderate shifts in process location. Finally, a real-life application is presented for quality practitioners to illustrate the effectiveness of the proposed control chart.

Inference for a Progressive-Stress Model Based on Ordered Ranked Set Sampling under Type-II Censoring

The progressive-stress accelerated life test is discussed under the ordered ranked set sampling procedure. It is assumed that the lifetime of an item under use stress is exponentially distributed and the law of inverse power is considered as the relationship between the scale parameter and the applied stress. The involved parameters are estimated using the Bayesian technique, under symmetric and asymmetric loss functions, based on ordered ranked set samples and simple random samples subject to type-II censoring. Real and simulated data sets are used to illustrate the theoretical results presented in this paper. Finally, a simulation study followed by numerical calculations is performed to evaluate the Bayesian estimation performance based on the two sampling types.

Bayesian Estimation of the Scale Parameter of Weibull Distribution using Ranked Set Samples

This research article is primarily focused on the investigation of Bayes estimators for the scale parameter of the Weibull distribution. Specifically, we focus on a sampling method known as Ranked Set Sample with Unequal Samples (RSSU), as introduced and studied by Bhoj (2001). Our objective is to derive Bayes estimates for the scale parameter utilizing two distinct loss functions: the squared error loss (SEL) function and the linear exponential (LINEX) loss function. We consider the scenario where the scale parameter follows either a gamma prior distribution or a Jeffreys prior distribution. To evaluate the performance of these estimators, we conduct simulations and analyse their bias and mean squared error (MSE). Our findings show that RSSU-based estimators outperform those based on Simple Random Sampling (SRS) and Ranked Set Sampling (RSS), when either Jeffreys prior or gamma prior distribution is used.

Information theory approach to ranked set sampling and new sub-ratio estimators

In this study, we introduce a new approach to the mean estimators in ranked set sampling. The amount of information carried by the auxiliary variable is measured with the Shannon entropy method on populations and samples and to use this information in the estimator, the basic ratio and the generalized exponential ratio estimators are modified as sub-ratio estimators to use only the information on the sample. Without using the required population parameter for ratio estimators, we propose new sub-ratio type estimators using only the auxiliary variable for ranking in the implementation of the ranked set sampling method. The mean squared errors and bias formulas of the proposed estimators are obtained and it is shown that the proposed estimators are more efficient than the classic mean estimator and ratio estimator of RSS under the certain theoretical conditions. Simulation and real data studies also show that the proposed estimators always give better results than the mean estimators of ranked set sampling and it is observed that the relative efficiencies of the proposed estimators increase depending on the magnitude of the entropy, the correlation between the auxiliary and the study variables, and the set sizes.

Parameter Estimation of the Exponentiated Pareto Distribution Using Ranked Set Sampling and Simple Random Sampling

In this paper, we have considered that ranked set sampling is able to estimate the parameters of exponentiated Pareto distribution. The method with which the maximum likelihood estimators for the parameters of exponentiated Pareto distribution is studied is numerical since there is no presence or possibility of a closed-form at the hands of estimators or any other intellectual. The numerical approach is a well-suited one for this study as there has been struggles in achieving it with any other technique. In order to compare the different sampling methods, simulation studies are performed as the main technique. As for the illustrative purposes, analysis of a simulated dataset is desired for the objective of the presentation. The conclusion that we can reach based on these is that the estimators based on the ranked set sample have far better efficiency than the simple random sample at the same sample size.

Improved Nonparametric Control Chart Based on Ranked Set Sampling with Application of Chemical Data Modelling

The statistical performance of parametric control charts is questionable when the underlying process does not follow any specified probability distribution. Nonparametric control charts are the best substitute for this situation. On the other hand, the ranked set sampling technique is preferred over the simple random sampling technique because it reduces the variability of process parameters and improves the control chart’s performance. This study aims to offer a nonparametric double homogeneously weighted moving average control chart under Wilcoxon signed-rank test considering the ranked set sampling technique (regarded as NPDHWMA RSS ), to further enhance the process location monitoring. The proposed chart’s run-length performance is compared with competing control charts, such as DEWMA- X ¯ , NPDEWMA-SR, NPRDEWMA-SR, DHWMA, and NPHWMA RSS control charts. The comparison revealed that the proposed NPDHWMA RSS control chart outperformed the other competing control charts, particularly for small to moderate shifts in process location. Finally, a real-life application is also offered for quality practitioners to show the strength of the proposed control chart.

Design-based estimators of the distribution function in ranked set sampling with an application

Empirical distribution functions (EDFs) based on ranked set sampling (RSS) and its modifications have been examined by many authors. In these studies, the proposed estimators have been investigated for infinite population settings. However, developing EDF estimators in finite population settings would be more valuable for areas such as environmental, ecological, agricultural, biological, medical, etc. This paper introduces new EDF estimators based on level-0, level-1 and level-2 sampling designs in RSS. Asymptotic properties of the new EDF estimators have been established. Numerical results have been obtained for the case when ranking is imperfect under different distribution functions. It has been observed that level-2 sampling design provides a more efficient EDF estimator than its counterparts of level-0, level-1 and simple random sampling. In real data application, we consider a pointwise estimate of distribution function and estimation of the median of sheep's weights at 7 months using RSS based on level-2 sampling design.

New Exponential Ratio Estimator in Ranked Set Sampling

In this study, we adapted the families of estimators from Ünal and Kadilar (2021) using the exponential function for the population mean in case of non-response for simple random sampling for the estimation of the mean of the population with the RSS (ranked set sampling) method. The equations for the MSE and the bias of the adapted estimators are obtained for RSS and it in theory shows that the proposed estimator is additional efficient than the present RSS mean estimators in the literature. In addition, we support these theoretical results with real COVID-19 real data and conjointly the simulation studies with different distributions and parameters. As a result of the study, it was observed that the efficiency of the proposed estimator was better than the other estimators.

Generalized ratio-cum-product type exponential estimation of the population mean in median ranked set sampling.

Generalized ratio-cum-product type exponential estimation of the population mean in median ranked set sampling.

On weighted extropy of ranked set sampling and its comparison with simple random sampling counterpart

The extropy measure proposed by Lad, Sanfilippo, and Agro (Statistical Science 30 (1):40–58, 2015) as a dual function of Shannon entropy has received a considerable attention in the last five years. In this paper, we first show a representation for the weighted extropy of ranked set sampling in terms of quantile and density-quantile functions. Then we provide some related results including monotone properties, stochastic orders, characterizations and sharp bounds. Moreover, the so obtained results show how the weighted extropy of ranked set sampling compares with its counterpart of simple random sampling.

Empirical likelihood inference for area under the receiver operating characteristic curve using ranked set samples.

The area under a receiver operating characteristic curve (AUC) is a useful tool to assess the performance of continuous-scale diagnostic tests on binary classification. In this article, we propose an empirical likelihood (EL) method to construct confidence intervals for the AUC from data collected by ranked set sampling (RSS). The proposed EL-based method enables inferences without assumptions required in existing nonparametric methods and takes advantage of the sampling efficiency of RSS. We show that for both balanced and unbalanced RSS, the EL-based point estimate is the Mann-Whitney statistic, and confidence intervals can be obtained from a scaled chi-square distribution. Simulation studies and two case studies on diabetes and chronic kidney disease data suggest that using the proposed method and RSS enables more efficient inference on the AUC.

On estimating the area under the ROC curve in ranked set sampling

In medical research, the receiver operating characteristic curve is widely used to evaluate accuracy of a continuous biomarker. The area under this curve is known as an index for overall performance of the biomarker. This article develops three new estimators of the area under the receiver operating characteristic curve in ranked set sampling. The first estimator is obtained under normality assumption. The two other estimators are constructed by applying a Box-Cox transformation on data, and then using either a parametric estimator or a kernel-density-based estimator. A simulation study is carried out to compare the proposed estimators with those available in the literature. It emerges that the new estimators offer some advantages in specific situations. Application of the methods is demonstrated using real data in the context of medicine.

Parametric estimation of location and scale parameters based on ranked set sampling with unequal set sizes

Ranked set sampling with unequal set sizes (RSSU) are some of the important variants of ranked set sampling with equal set sizes (RSS). The sets that arise naturally in many applications are typically of different set sizes. One may prefer to use the largest sets available naturally along with the smaller sets rather than an attempt to form artificial equal-sized sets. This article develops maximum likelihood estimators for the location-scale family of distributions based on ranked set sampling with unequal set sizes (RSSU). The closed form expressions for MLE under RSSU do not exist, we have proved the existence of MLE for location and scale parameters for some standard distributions for RSSU data. It is proved that MLE based on MedRSSU are more efficient than their counterparts based on SRS for some standard distributions for location-scale parameters. It is also shown that asymptotic efficiencies of the MLE based on MedRSSU are considerably better than those of the estimators based on RSS with the same number of observations. A simulation study is conducted to compare the performances of the MLE’s from RSS and MedRSSU with the corresponding SRS estimators when the underlying distributions are normal and logistic.

On the Generalized Bilal Distribution: Some Properties and Estimation under Ranked Set Sampling

The generalized Bilal (GB) distribution can be defined as the distribution of the median of three independent random variables drawn from the Weibull distribution. Its failure rate function can be monotonic (decreasing or increasing) or upside-down bathtub-shaped. In this study, we aim to reveal some important properties of the GB distribution that have not been considered before. The findings are both theoretical and practical. From the theoretical viewpoint, we present explicit expressions for both single and product moments of order statistics from the GB distribution. The L-moments are derived as well. From the practical viewpoint, the parameter estimations are accomplished using the maximum likelihood (ML) method, which is based on two different sampling schemes: simple random sampling (SRS) and ranked set sampling (RSS) schemes. Furthermore, the asymptotic confidence intervals for the SRS and RSS estimators are discussed. For the sake of comparison and illustration, a simulation study and a real data example are presented. Concluding remarks are given at the end.

Some Efficient Methods to Remove Bias in Ratio and Product Types Estimators in Ranked Set Sampling

Ranked set sampling is one method to potentially increase precision and reduce costs by using quantitative or qualitative information to obtain a more representative sample. Use of auxiliary information has shown its significance in improvement of efficiency of estimators of unknown population parameters. Ratio estimator is used when auxiliary information in the form of population mean of auxiliary variable at estimation stage for the estimation of population parameters when study and auxiliary variable are positively correlated. In case of negative correlation between study variable and auxiliary variable, Product estimator is defined for the estimation of population mean. This paper proposed the problem of reducing the bias of the ratio and product estimators of the population mean in ranked set sampling (RSS). This paper suggested several type unbiased estimators of the finite population mean using information on known population parameters of the auxiliary variable in ranked set sampling. An important objective in any statistical estimation procedure is to obtain the estimators of parameters of interest with more precision. The Variance of the proposed unbiased ratio and product estimators are obtained up to first degree of approximation. Theoretically, it is shown that these suggested estimators are more efficient than the unbiased estimators in Simple random sampling. A numerical illustration is also carried out to demonstrate the merits of the proposed estimators using RSS over the usual estimators in SRS.

Estimating System Reliability Using Neoteric and Median RSS Data for Generalized Exponential Distribution

In this work, we show how to estimate stress strength (SS) reliability when the stress (Y) and strength (X) distributions are generalized exponentials with a common scale parameter. The SS reliability estimator is considered in view of neoteric ranked set sampling (NRSS) and median ranked set sampling (MRRS). We acquire an estimate of the reliability (R) when such samples of the stress and strength random variables are gathered using the same NRSS technique. Furthermore, the reliability estimator is derived when the stress distribution data are in the pattern of MRSS with just an odd/even set size and the strength distribution data are derived from NRSS and vice versa. The simulation results are used to evaluate and understand the adequacy of a variety of estimators for the suggested schemes. Based on our simulated results, we found that NRSS-based stress strength reliability estimates are more efficient than MRSS-based stress strength reliability estimates. The analysis of real-world data is used to implement the recommended estimators.

Estimation of distribution function using L ranked set sampling and robust extreme ranked set sampling with application to reliability

Estimation of distribution function using L ranked set sampling and robust extreme ranked set sampling with application to reliability

Predictive estimation approach using difference and ratio type estimators in ranked set sampling

In this article, we introduce the predictive estimation approach for estimating the population mean using modified difference and ratio type predictive estimators in ranked set sampling. The expressions of bias and mean square error of the proffered predictive estimators are reported to the first order of approximation. A comparative study of the proffered predictive estimators with the conventional predictive estimators under simple random sampling and ranked set sampling is considered. The theoretical findings have been supported by a broad spectrum computational study carried out using various real and simulated data sets. Further, the appropriate suggestions are forwarded to the survey professionals.

Estimation of the population distribution function using varied L ranked set sampling

A generalized ranked set sampling (RSS) plan has recently been provided in the literature called varied L RSS (VLRSS). It is shown that VLRSS encompasses several existing RSS variations and also it efficiently estimates the population mean. In this article, we extend the work and consider estimating the cumulative distribution function (CDF) using VLRSS. Three new CDF estimators are proposed and their asymptotic properties are also theoretically investigated. Taking into account the information supported by the unmeasured sampling units, we also propose a general class of CDF estimators. Using small Monte Carlo experiments, we study the behavior of the proposed CDF estimators with respect to the conventional CDF estimator under RSS. It is found that the conventional RSS-based CDF is outperformed by at least one of VLRSS-based CDF estimators in most of the considered cases. Finally, an empirical example is utilized to illustrate the potential application of the proposed estimators.

A Suggestion for Using Ranked Set Sampling in Household Expenditure and Income Survey

The ranked set sampling method uses the ranking information of the units to provide a more representative sample of the population to the survey designers. The sampling distribution is closer to the actual distribution of the population. In this article, to ensure the effectiveness of ranked set sampling in extensive surveys conducted to prepare official statistics, we intend to use this sampling method to improve the efficiency of key estimates of household expenditure and income survey of the Statistics Center of Iran. The results show that using ranked set sampling to design household expenditure and income surveys can improve the efficiency of key estimates of the study, provided that the ranking variable used has a high correlation with the main variables of the study. Obviously, in the absence of a suitable and available variable for ranking the units, the information of the sampling frame can be used to construct a ranking variable correlated with the key variables of the survey.