Ranked Set Sampling Technique Research Articles

Estimation methods based on ranked set sampling for the power logarithmic distribution

The sample strategy employed in statistical parameter estimation issues has a major impact on the accuracy of the parameter estimates. Ranked set sampling (RSS) is a highly helpful technique for gathering data when it is difficult or impossible to quantify the units in a population. A bounded power logarithmic distribution (PLD) has been proposed recently, and it may be used to describe many real-world bounded data sets. In the current work, the three parameters of the PLD are estimated using the RSS technique. A number of conventional estimators using maximum likelihood, minimum spacing absolute log-distance, minimum spacing square distance, Anderson-Darling, minimum spacing absolute distance, maximum product of spacings, least squares, Cramer-von-Mises, minimum spacing square log distance, and minimum spacing Linex distance are investigated. The different estimates via RSS are compared with their simple random sampling (SRS) counterparts. We found that the maximum product spacing estimate appears to be the best option based on our simulation results for the SRS and RSS data sets. Estimates generated from SRS data sets are less efficient than those derived from RSS data sets. The usefulness of the RSS estimators is also investigated by means of a real data example.

Statistical inference for a novel distribution using ranked set sampling with applications

Working on symmetrical or asymmetrical data is complicated since each requires a different probability density function. Many statistical distributions can be used for these data types, where choosing one should be satisfied with the correct data type. So, we apply the ranked set sampling technique, which is essential in gaining data when dealing with units in a population is expensive. However, their classification is simple according to the variable of interest. The Unit Generalized Rayleigh distribution has recently played a crucial role in analyzing symmetrical or asymmetrical complex data sets specifically in modeling claim and risk data used in actuarial and financial studies, and its density can take different symmetric and asymmetric possible shapes. It is proposed in various areas, such as reliability, survival, economics, actuarial science, and insurance. We applied the ranked set sampling design in this article for gaining the model parameter estimations of the unit generalized Rayleigh model. Different estimation procedures and risk measures are computed. Moreover, the performance of these measures is illustrated via numerical simulation experiments. Under different proposed estimators, we conduct the validation of the suggested ranked set sampling design via numerous Monte Carlo simulation experiments by computing average bias and mean squared errors. At the end, we illustrated two real applications of the financial area for demonstrating the potential and the supremacy of the proposed ranked set sampling estimators.

General weighted cumulative residual (past) extropy of minimum (maximum) ranked set sampling with unequal samples

The general weighted cumulative residual extropy (GWCRJ) and general weighted cumulative past extropy (GWCPJ) are introduced in this article. There are some results in relation to GWCPJ and GWCRJ. We take into account GWCRJ-based uncertainty measures for the minimal ranked set sampling technique with unequal samples (minRSSU). Additionally, we take into account GWCPJ-based uncertainty measures for the maximum ranked set sampling technique with unequal samples (maxRSSU). Stochastic comparison for simple random sampling (SRS) is discussed. We looked at the monotone properties of minRSSU and maxRSSU as well as stochastic comparison. The empirical estimators of GWCPJ and GWCRJ are obtained and a simulation study for comparing the proposed estimator will be given involving the proposed ranked set sampling schemes under perfect ranking.

Estimation of Population Size Using Ranked Set Sampling and Some of its Variations

The purpose of this paper is to estimate the population size of known total, using a sample that chosen using ranked set sampling technique and some of its variations; in particular, Ranked Set Sampling (RSS), Moving Extreme Ranked Set Sampling (MERSS) and Median Ranked Set(MRSS) are considered. The estimators obtained are compared with their counterparts using simple random sampling(SRS). It turned out that the estimators using RSS and its variations are more efficient than the corresponding estimators using SRS.

Estimation of the Location Parameter of Cauchy Distribution Using Some Variations of the Ranked Set Sampling Technique

Estimation of the Location Parameter of Cauchy Distribution Using Some Variations of the Ranked Set Sampling Technique

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.

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.

Comparison Between Dependent and Independent Ranked Set Sampling Designs for Parametric Estimation with Applications

This paper is concerned with the estimation problem using maximum likelihood method of estimation for the unknown parameters of exponetiated gumbel distribution based on neoteric ranked set sampling (NRSS) as a new modification of the usual ranked set sampling (RSS) technique. Numerical study is conducted to compare NRSS as a dependent ranked set sampling technique, with RSS, and median ranked set sampling as independent sampling techniques, and then the performance of RSS and its modifications will be compared with simple random sampling based on their mean square errors and efficiencies.

New EWMA S2 Control Charts for Monitoring Process Dispersion

The Exponentially Weighted Moving Average (EWMA) control chart is an effective tool for the detection of small shifts in the process variability. This research studied the properties of EWMA charts based on unbiased sample variance, S-2, for monitoring of changes in the process dispersion. However, since an increase in process variance could lead to an increased number of defective products, we only considered upward shifts in the process variance. The proposed schemes were based on simple random sampling and extreme variations of ranked set sampling technique for efficient monitoring. Using Monte Carlo simulations, we compared the relative performance of EWMA charts based on unbiased sample variance, S-2, and its logarithmic transformation ln(S-2) as well as some existing schemes for monitoring the increases in variability of a normal process. It is found that the proposed schemes significantly outperform several other procedures for detecting increases in the process dispersion. Numerical example is given to illustrate the practical application of the proposed schemes using real industrial data.

A New Combined Shewhart–Cumulative Sum S Chart for Monitoring Process Standard Deviation

The combined application of a Shewhart chart and cumulative sum (CUSUM) control chart is an effective tool for the detection of all sizes of process shifts as the scheme combines the advantages of a CUSUM at detecting small to moderate shifts and Shewhart for the quick detection of very large shifts. This article proposes new combined Shewhart–CUSUM S charts based on the extreme variations of ranked set sampling technique, for efficient monitoring of changes in the process dispersion. Using Monte Carlo simulations, the combined scheme is designed to minimize the average extra quadratic loss over the entire process shift domain. The results show that the combined Shewhart–CUSUM S charts uniformly outperform several other procedures for detecting increases and decreases in the process variability. Moreover, the proposed scheme can detect changes that are small enough to escape the Shewhart S chart or fairly large to escape detection by the CUSUM S chart. Numerical example is given to illustrate the practical application of the proposed scheme using real industrial data. Copyright © 2015 John Wiley & Sons, Ltd.

Estimation of the scale parameter of a log-logistic distribution

In this work the ranked set sampling technique has been applied to estimate the scale parameter \(\alpha \) of a log-logistic distribution under a situation where the units in a sample can be ordered by judgement method without any error. We have evaluated the Fisher information contained in the order statistics arising from this distribution and observed that median of a random sample contains the maximum information about the parameter \(\alpha \). Accordingly we have used median ranked set sampling to estimate \(\alpha \). We have further carried out the multistage median ranked set sampling to estimate \(\alpha \) with improved precision. Suppose it is not possible to rank the units in a sample according to judgement method without error but the units can be ordered based on an auxiliary variable \(Z\) such that \((X, Z)\) has a Morgenstern type bivariate log-logistic distribution (MTBLLD). In such a situation we have derived the Fisher information contained in the concomitant of rth order statistic of a random sample of size \(n\) from MTBLLD and identified those concomitants among others which possess largest amount of Fisher information and defined an unbalanced ranked set sampling utilizing those units in the sample and thereby proposed an estimator of \(\alpha \) using the measurements made on those units in this ranked set sample.

Cautionary note on unbalanced ranked-set sampling

Balanced ranked-set sampling (RSS) offers improved statistical inference in situations where the units to be sampled can be ranked relative to each other prior to formal measurement. Recent work has shown that provided the ranking process is perfect, unbalanced RSS can do even better. In this article, we examine the performance of one unbalanced RSS technique when the ranking process is not perfect. Using an Ohio corn production data set, we show that median-based unbalanced RSS outperforms balanced RSS in estimating a population median if the rankings are nearly perfect. We also show, however, that median-based unbalanced RSS may perform extremely poorly when the ranking process is less than perfect. This effect is particularly pronounced when the variable of interest has a skewed distribution. We thus offer a note of caution for users of unbalanced RSS.

Estimation of the means of the bivariate normal using moving extreme ranked set sampling with concomitant variable

The estimation of the means of the bivariate normal distribution, based on a sample obtained using a modification of the moving extreme ranked set sampling technique (MERSS) is considered. The modification involves using a concomitant random variable. Nonparametric-type methods as well as the maximum likelihood estimation are considered. The estimators obtained are compared to their counterparts based on simple random sampling (SRS). It appears that the suggested estimators are more efficient. Also, MERSS with concomitant variable is easier to use in practice than the usual ranked set sampling (RSS) with concomitant variable. The issue of robustness of the procedure is addressed. Real trees data set is used for illustration.