Double Ranked Set Sampling Research Articles

Modified median quartile double ranked set sampling for estimation of population mean

Environmental monitoring and assessment aim to gather data economically, without bias, using efficient and cost-effective sampling methods. One such traditional method is Ranked Set Sampling (RSS), often employed to achieve observational economy. This article introduces an innovative two-stage sampling approach for ranked set sampling (RSS) to get a more precise estimate of the population mean. Modified Median Quartile Double Ranked Set Sampling (MMQDRSS) highlights the ranked base technique's potential as a cost-effective sampling method. To evaluate the performance of the proposed estimator by using real-life data and conducting a simulation study to compare the relative efficiency of the proposed estimator with some existing methods.

Statistical inference for the bathtub-shaped distribution using balanced and unbalanced sampling techniques

<p>In order to reduce errors and enhance precision while estimating the unknown parameters of the distributions, it is crucial to choose a representative sample. The common estimation methods that estimate the parameters associated with the bathtub-shaped distribution include maximum likelihood (ML), maximum product of spacings estimation (MPSE), and Cramér-von Mises estimation (CME) methods. However, four modifications are used with the sample selection technique. They are simple random sampling (SRS), ranked set sampling (RSS), maximum ranked set sampling (MaxRSS), and double ranked set sampling (DBRSS), which is due to small sample sizes. Based on the estimation methods such as ML, MPSE, and CME, the ranked set sampling techniques do not have simple functions to manage them. The MaxRSS matrix has variable dimensions but requires fewer observations than RSS. DBRSS requires a greater number of observations than MaxRSS and RSS. According to simulation studies, the RSS, MaxRSS, and DBRSS estimators were more effective than the SRS estimator for different sample sizes. Additionally, MaxRSS was discovered to be the most efficient RSS-based technique. Other techniques, however, proved more effective than RSS for high mean squared errors. The CM method estimated the true values of the parameters more accurately and with smaller biases than ML and MPSE. The MPSE method was also found to have significant biases and to be less accurate in estimating the values of the parameters when compared to the other estimate methods. Finally, two datasets demonstrated how the bathtub-shaped distribution could be feasible based on different sampling techniques.</p>

Dual-rank ranked set sampling

In this paper, we propose a new sampling design extending the well-known ranked set sampling, which we named dual-rank ranked set sampling. Unlike the original ranked set sampling scheme, dual-rank ranked set sampling is based on two ranking sets stages, as the double ranked set sampling design. Dual-rank ranked set sampling differs from double ranked set sampling, however, since it requires only n 2 initially selected units to draw a sample of size n, whereas double ranked set sampling is based on n 3 units to provide a sample of similar size. We verified that the dual-rank ranked set sampling sample estimator of the population mean is an unbiased estimator for the corresponding population parameter when the underlying distribution is symmetric. A simulation study was carried out to evaluate the efficiency of dual-rank ranked set sampling. The simulation results pointed out that dual-rank ranked set sampling estimation is more efficient than simple random sampling and ranked set sampling, and it is a cost-effective alternative to double ranked set sampling estimation. The problem of interval estimation for dual-rank ranked set sampling was also addressed. An application based on fish ageing data is finally presented.

New mixed ranked set sampling variations

Building efficient sampling procedures to provide more accurate results with small sample sizes is one of the main goals in sampling surveys. The ranked set sampling (RSS) is a well‐known procedure for selecting representative samples and improving parametric estimation by employing ranking on observations. In order to have a more efficient sampling procedure, new sampling procedures are proposed and investigated in this article. The main focus of this article is to enhance the mean estimation of the study population using the proposed RSS procedures. The performance of the proposed sampling procedures is compared with their competitors in RSS, double RSS (DRSS), extreme RSS (ERSS), and double extreme RSS (DERSS) by conducting simulation studies for numerous (symmetric and asymmetric) distributions. An application to a real dataset is also considered to exemplify the achievement of the proposals. Numerical simulations show that the new modified estimators are unbiased for the population mean for symmetric distributions and they outperform their competitors in most of the cases investigated in this article.

Parameter Estimation Based on Double Ranked Set Samples with Applications to Weibull Distribution

In this paper, the likelihood function for parameter estimation based on double ranked set sampling (DRSS) schemes is introduced. The proposed likelihood function is used for the estimation of the Weibull distribution parameters. The maximum likelihood estimators (MLEs) are investigated and compared to the corresponding ones based on simple random sampling (SRS) and ranked set sampling (RSS) schemes. A Monte Carlo simulation is conducted and the absolute relative biases, mean square errors, and efficiencies are compared for the different schemes. It is found that, the MLEs based on DRSS is more efficient than MLE using SRS and RSS for estimating the two parameters of the Weibull distribution (WD).

Design of Improved EWMA Control Chart for Monitoring the Process Mean Using New Median Quartile Double Ranked Set Sampling

It is essential to monitor the mean of a process regarding quality characteristics for the ongoing production. For enhancement of mean monitoring power of the exponentially weighted moving average (EWMA) chart, a new median quartile double ranked set sampling (MQDRSS) based EWMA control chart is proposed and named as EWMA-MQDRSS chart. In order to study the performance of the developed EWMA-MQDRSS chart, performance measures; average run length, and the standard deviation of run length are used. The shift detection ability of the proposed chart has been compared with counterparts, under the simple random sampling and ranking based sampling techniques. The extensive simulation-based results indicate that the EWMA-MQDRSS chart performs better to trace all kinds of shifts than the existing charts. An illustrative application concerning monitoring the diameter of the piston ring of a machine is also provided to demonstrate the practical utilization of the suggested chart.

Design of Improved EWMA Control Chart for Monitoring the Process Mean Using New Median Quartile Double Ranked Set Sampling

It is essential to monitor the mean of a process regarding quality characteristics for the ongoing production. For enhancement of mean monitoring power of the exponentially weighted moving average (EWMA) chart, a new median quartile double ranked set sampling (MQDRSS) based EWMA control chart is proposed and named as EWMA-MQDRSS chart. In order to study the performance of the developed EWMA-MQDRSS chart, performance measures; average run length, and the standard deviation of run length are used. The shift detection ability of the proposed chart has been compared with counterparts, under the simple random sampling and ranking based sampling techniques. The extensive simulation-based results indicate that the EWMA-MQDRSS chart performs better to trace all kinds of shifts than the existing charts. An illustrative application concerning monitoring the diameter of the piston ring of a machine is also provided to demonstrate the practical utilization of the suggested chart.

Estimation of the Exponential Pareto Distribution’s Parameters under Ranked and Double Ranked Set Sampling Designs

In this paper, the derivation of the likelihood function for parameter estimation based on double ranked set sampling (DRSS) designs used by Sabry el.al.; (2019) for the estimation of the parameters of the power generalized Weibull distribution is considered. The developed likelihood function is then used for the estimation of the exponential Pareto distribution parameters. The maximum likelihood estimators (MLEs) are then investigated and compared to the corresponding ones based on simple random sampling (SRS) and ranked set sampling (RSS) designs. A Monte Carlo simulation is conducted and the absolute relative biases, mean square errors, and efficiencies are compared for the different designs. The relative efficiency of the DRSS estimates with respect to other designs was found to be higher in case of the exponential Pareto distribution (EP).

Joint monitoring of mean and variance under double ranked set sampling using likelihood ratio test statistic

Quality control charts are widely used as a process monitoring tool. In this article, an attempt is made to develop a new control chart that integrates the exponentially weighted moving average procedure with the generalized likelihood ratio test statistic for joint monitoring of process mean and dispersion under double ranked set sampling. A Monte Carlo simulation study is conducted to evaluate the proposed control chart based on average run length and the standard deviation of the run length. The performance of the proposed chart is examined as compared to ranked set sampling (RSS) and pair ranked set sampling (PRSS) based control charts when detecting shifts in the process mean and variability. Results showed that the proposed control chart performs better than the existing RSS- and PRSS-based control chart in simultaneous detection of shifts in the process mean and variability. An application to the real data is provided to illustrate the implementations of the proposed and existing control charts.

Developing Mixed EWMA-CUSUM and CUSUM-EWMA control charts based on MRSS and DRSS procedures

The mixed EWMA-CUSUM and CUSUM-EWMA control charts are among the control charts provided in recent years by combining two exponentially weighted moving average and cumulative sum charts for efficient monitoring of the process mean. In this paper, we extended these mixed control charts by using new median ranked set sampling and double ranked set sampling procedures. The performance of the proposed mixed control charts is evaluated through extensive Monte Carlo simulations in terms of average run length criterion and the results show the proposed charts outperform the similar charts for detecting different shifts in process mean. Furthermore, a real data-set is also presented for explaining the implementation of the proposed control charts.

Evaluation of Cpm estimators in ranked set sampling designs

Capability analysis allows evaluating the conformity of the production to the project specifications in industrial processes. Different indices can be used to assess the process capability, among them the Cpm (or Taguchi) index. In this work we propose the estimation of Cpm for normally distributed processes using ranked set sampling (RSS) and two extensions: pair ranked set sampling (PRSS), as an economical alternative; and double ranked set sampling (DRSS), as a more efficient (and expensive) strategy. Also, three different Cpm estimators were considered. Their performances regarding bias, mean squared error, and relative efficiency were evaluated through Monte Carlo simulation. The results indicated that: (i) There was a substantial variation in performances for different Cpm estimators, particularly for small samples; (ii) RSS based estimators outperformed their simple random sampling counterparts; (iii) DRSS estimator presented the lowest mean square error; and (iv) PRSS estimator showed competitive performance to its counterparts in different scenarios.

Influence on Estimation of Mean by Using Quartile Paired Double Ranked Set Sampling

In this paper, we present an efficient quartile paired double ranked set sampling (QPDRSS) scheme to estimate the population mean. QPDRSS provides an unbiased improved population mean estimator when the distribution is symmetric and bears negligible biasness for non-symmetric distribution. The performance of the proposed mean estimator is compared to its competitors in simple random sampling, double ranked set sampling, extreme paired double ranked set sampling and paired double ranked set sampling by manipulating simulation process for various (symmetric and non-symmetric) distributions. A real dataset is also studied to exemplify the achievement of the proposal.

Practicality of Some Variations of Ranked Set Sampling

Judgement ranking in ranked set sampling (RSS) and its variations depends on the ability of an observer to rank a set of objects according to the study variable without doing any actual measurement. In practice, and in some variations of RSS, it is hard to assign these ranks. In this paper, we discuss the practicality of ranking some extensions of RSS such as median RSS, double median RSS, and double RSS. The Hellinger distance is used as a measure of practicality. Although double median RSS is the most efficient approach among the RSS variations considered, it is shown in this paper that it is the least practical.

Enhancing the performance of exponential weighted moving average control chart using paired double ranked set sampling

The exponentially weighted moving average (EWMA) control chart is good enough to capture a small/moderate shift in the process-mean as it has the ability to provide good detection of a said shift by using current as well as past information about the process. To enhance the performance of EWMA chart, cost-effective and efficient ranked set sampling (RSS) type methods, named paired double-RSS (PDRSS), extreme paired double-RSS (EPDRSS) and quartile paired double-RSS (QPDRSS) are used to propose EWMA-PDRSS, EWMA-EPDRSS and EWMA-QPDRSS charts. By using the simulation study, the performance of developed control charts is evaluated in terms of average run length (ARL) as well as standard deviation of run length (SDRL) measures. The simulation results revealed that the proposed charts surpass the simple random sampling (SRS) based classical EWMA (EWMA-SRS) chart when capturing a small/moderate shift in the process-mean. An illustrative application is also presented to support the proposed study.

Further Improving the Performance of Logistic Regression Analysis Using Double Extreme Ranking

For dichotomous or ordinal dependent variables, logistic regression models as one of the generalized linear models have been intensively applied in several fields. We proposed a more powerful performance of logistic regression model analysis when a modified extreme ranked set sampling (modified ERSS) is used and further improved the performance when a modified double extreme ranked set sampling (modified DERSS) is used. We assume that ranking could be performed based on an available and easy-to-rank auxiliary variable, which is associated with the response variable. Theoretically and by simulations, we showed the superiority of the performance of the logistic regression analysis when ERSS and DERSS are used compared with using the simple random sample. We illustrated the procedures developed using real data from the 2011/12 National Survey of Children’s Health.

Estimation of population mean under different stratified ranked set sampling designs with simulation study Application to BMI Data

In this article, we have compared the performance ratio-type estimators in some stratified ranked set sampling methods. These sampling methods are stratified random sampling, stratified ranked set sampling, stratified double ranked set sampling and stratified median ranked set sampling. In these methods, the ratio type estimators using auxiliary variable information such as coefficient of variation and kurtosis are examined. We have used a real data set to see the performance of estimators. We use the data concerning body mass index (BMI) as a study variable and the age and the weight as auxiliary variables for 800 people in Turkey in 2014. We stratified the data set using gender. A simulation study is carried out to see performance of the proposed ratio type estimators in these stratified ranked set sampling designs. The performances of these estimators are compared in terms of mean squared error (MSE) and percent relative efficiency (PRE). The importance of this study is that, a detail simulation study is done using a real data set and compare these stratified sampling designs in a study in the sampling literature.

Efficient control charts for monitoring the process mean using different paired double ranked set sampling designs

Efficient monitoring of process mean using a cost-effective sampling design is a great achievement in industries to maintain their products quality. The aim of this study is to improve the existing mean control charting structures by implementing efficient and cost-effective paired double ranked set strategies. To detect and examine the fluctuations in the production process efficiently, three new mean control charts based on paired double ranked set sampling (PDRSS), extreme paired double ranked set sampling (EPDRSS) and quartile paired double ranked set sampling (QPDRSS) designs are suggested. By using different performance measures, the efficiency of the proposed and considered charts is compared on the basis of simulated as well as real data. The findings revealed that the performance of proposed mean chart based on QPDRSS is superior to all single and mentioned double ranked set sampling mean control charts.

Novel entropy estimators of a continuous random variable

This paper presents some novel entropy estimators of a continuous random variable using simple random sampling (SRS), ranked set sampling (RSS), and double RSS (DRSS) schemes. The theoretical results of the proposed entropy estimators are derived. The proposed entropy estimators are compared in terms of the bias and the root mean squared errors, theoretically and numerically, with the Vasicek O. [A test for normality based on sample entropy, J. R. Stat. Soc. B 38:54–59, 1976.] entropy estimators using SRS, RSS, and DRSS schemes. It turns out that the new novel entropy estimators are substantially better than the existing Vasicek’s entropy estimators.

Efficient Phase II Monitoring Methods for Linear Profiles Under the Random Effect Model

A profile is a functional relationship between two or more variables used to monitor the process performance and its quality. Sometimes, the aforementioned relationship is linear or nonlinear depending upon the situation. A monitoring method based on the linear profiles is known as linear profiling which is commonly used due to its simplicity and efficacy. Linear profiling methods have been studied by many researchers with a fixed effect model. However random effect model provides a more suitable interpretation as compared to the fixed effect model under different real-time monitoring methods. Therefore in this article, we are intended to propose a linear profiling EWMA method (EWMA <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">χ[R]</sub> -3 chart) and MEWMA <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x[R]</sub> chart based on the random effect model using different ranked set sampling techniques such as ranked set sampling (RSS), extreme RSS (ERSS), median RSS (MRSS), double RSS (DRSS), double ERSS (DERSS) and double MRSS (DMRSS). The ranked set sampling (RSS) schemes are not only cost-effective method but also an efficient mechanism as compared to simple random sampling. A designed simulation study used Average Run Length (ARL) as an evaluation measure to witness the detection ability of newly offered EWMA <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x[R]</sub> -3 chart, MEWMA <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x[R]</sub> chart and existing EWMA <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x[SRS</sub> ]-3 chart. The extensive simulation showed that the proposed EWM <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Ax[R]</sub> -3 chart and MEWMA <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x[R</sub> ] chart have superiority to detect faults in the process compared to a competitive counterpart. The results are further justified with real data application related to a combined cycle power plant.

Investigating the Efficiency of Teaching Mathematics to Students by Using the Double Ranked Set Sampling

The main objective of this paper is to evaluate the efficacy of double ranked set sampling method in teaching mathematics to the students. The notion of ranked set sampling for estimating the mean of a population and its advantage over the use of a simple random sampling for the sampling is established in the literature. Furthermore, the double ranked set sampling has proven to be even more efficient than RSS. In this research, we review the use of the DRSS to estimate the intercept, the slope, and the standard deviation of the error terms as parameters of a simple linear regression model of teaching mathematics to students, when replications exist at each value of the predictor. Finally, we illustrate the proposed procedure by applying it when the underlying distribution of the error terms is normal or Laplace. Regardless of the assumed number of replications in the experiment, we observe a substantial gain in relative precision while using DRSS procedure over using RSS technique.