Varied L Ranked Set Sampling Scheme

The control charts with the Ranked Set Sampling (RSS) scheme performs better in detecting shifts in mean and variance of the process compared to the control charts with the Simple Random Sampling scheme (SRS). In this article, we develop a Novel Shewhart type simultaneous univariate control chart (Max Chart) based on the RSS scheme. Since the distribution of the statistics based on the RSS scheme is not known, an alternative approach is taken by using an improved bootstrap method in developing a novel Shewhart type simultaneous control chart based on RSS. The results of the Monte Carlo simulation study show that, when compared to the conventional Max chart based on the SRS scheme, the average run length under out-of-control conditions (ARL1) obtained from that the Improved Bootstrap Max Chart based on the RSS scheme is superior in detecting shifts in mean and variance of the process. A real case example is also given to illustrate the operation and performance of the proposed control chart. Key points:1.A novel Shewhart type simultaneous univariate control chart (Max Chart) based on the RSS scheme is proposed to improve the performance of the of control chart in detecting process shifts.2.The Control limit of Shewhart type simultaneous univariate control chart (Max Chart) based on the RSS scheme was constructed using an Improved Bootstrap method.

ABSTRACTRecently, a hybrid ranked set sampling (HRSS) scheme has been proposed in the literature. The HRSS scheme encompasses several existing ranked set sampling (RSS) schemes, and it is a cost-effective alternative to the classical RSS and double RSS schemes. In this paper, we propose an improved estimator for estimating the cumulative distribution function (CDF) using HRSS. It is shown, both theoretically and numerically, that the CDF estimator under HRSS scheme is unbiased and its variance is always less than the variance of the CDF estimator with simple random sampling (SRS). An unbiased estimator of the variance of CDF estimator using HRSS is also derived. Using Monte Carlo simulations, we also study the performances of the proposed and existing CDF estimators under both perfect and imperfect rankings. It turns out that the proposed CDF estimator is by far a superior alternative to the existing CDF estimators with SRS, RSS and L-RSS schemes. For a practical application, a real data set is considered on the bilirubin level of babies in neonatal intensive care.

This study is focused on ranked set sampling theory which is constructive and cost efficient. Estimation for population mean for different sample sizes based on new ranked set sampling (NRSS) scheme is explored. A simulation study has been conducted and a comparison has been made with simple random sampling (SRS), ranked set sampling (RSS), extreme ranked set sampling (ERSS) and quartile ranked set sampling (QRSS) for normal and non – normal distributions.

Stress-strength models are considered of great significance due to their applicability in varied fields. We address the estimation of the system reliability of a multicomponent stress-strength model, say Rs,k, of an s out of k system when the pair stress and strengths are drawn from a generalized inverted exponential distribution. The system is deemed as working if at least s out of k strengths be more than its stress. We obtain the reliability estimators when the data of strength and stress distributions are collected from three sampling schemes, specifically; simple random sampling, ranked set sampling, and median ranked set sampling. We obtain four estimators of Rs,k out from median ranked set sampling. The behavior of different estimates is examined via a simulation study based on mean squared errors and efficiencies. The simulation studies point out that the reliability estimates of Rs,k, from the ranked set sampling scheme are preferred than other estimates picked from the simple random sample and median ranked set sampling in a majority of the situations. The theoretical studies are explained with the aid of real data analysis.

The neoteric ranked set sampling (NRSS) scheme is an effective design compared to the usually ranked set sampling (RSS) scheme. Herein, we regard reliability estimation of the stress-strength (SS) model using the maximum likelihood procedure via NRSS and RSS designs. Assume that stress Y and strength X are exponentiated exponential random variables with the same scale parameter. Various sample strategies are used to evaluate the reliability estimator. We acquire an estimate of R when the samples of stress and strength random variables are chosen from the same sampling methods, such as RSS or NRSS. Furthermore, we derive R estimator when X and Y are chosen from RSS and NRSS, respectively, and vice versa. A simulation investigation is formed to assay and compare the accuracy of estimates for all proposed schemes. We conclude based on study outcomes that the reliability estimates of the stress-strength model via NRSS are more efficient than the others via RSS. Analysis of real data is displayed to investigate the usefulness of the proposed estimators.

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.

The article introduces a novel Bayesian AEWMA Control Chart that integrates different loss functions (LFs) like the square error loss function and Linex loss function under an informative prior for posterior and posterior predictive distributions, implemented across diverse ranked set sampling (RSS) designs. The main objective is to detect small to moderate shifts in the process mean, with the average run length and standard deviation of run length serving as performance measures. The study employs a hard bake process in semiconductor production to demonstrate the effectiveness of the proposed chart, comparing it with existing control charts through Monte Carlo simulations. The results underscore the superiority of the proposed approach, particularly under RSS designs compared to simple random sampling (SRS), in identifying out-of-control signals. Overall, this study contributes a comprehensive method integrating various LFs and RSS schemes, offering a more precise and efficient approach for detecting shifts in the process mean. Real-world applications highlight the heightened sensitivity of the suggested chart in identifying out-of-control signals compared to existing Bayesian charts using SRS.

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.

To detect sustainable changes in the production processes, memory-type control charts are frequently utilized. This study is conducted to assess the performance of the Bayesian adaptive exponentially weighted moving average (AEWMA) control chart using ranked set sampling schemes following two different loss functions in the presence of a measurement error for posterior and posterior predictive distributions using conjugate priors. This study is based on the covariate model and multiple measurement methods in the presence of a measurement error (ME). The performance of the proposed Bayesian-AEWMA control chart with ME has been evaluated through the average run length and the standard deviation of the run length. Finally, a real-life application in semiconductor manufacturing was conducted to evaluate the effectiveness of the proposed Bayesian-AEWMA control chart with a measurement error based on different ranked set sampling schemes. The results demonstrate that the proposed control chart, in the presence of a measurement error, performed well in detecting out-of-control signals compared to the existing control chart. However, the median ranked set sampling scheme (MRSS) proved to be better than the other two schemes in the presence of a measurement error.

In survey sampling, obtaining a complete sampling frame that fully covers the target population is often challenging and costly. Multiple frame sampling provides a cost-effective and practical solution by combining two or more incomplete sampling frames to enhance coverage. This study introduces estimators that integrate Ranked Set Sampling (RSS), Extreme Ranked Set Sampling (ERSS), and Median Ranked Set Sampling (MRSS) within a dual-frame setup for estimating the population mean. The study describes the procedure for selecting samples from each frame, using ranking information, and then combining them to create an improved estimator. The methods presented are especially useful in large-scale surveys where obtaining a complete sampling frame is not feasible. An empirical investigation using real data evaluates the performance of above estimators based on dual-frame simple random sampling (DF-SRS). In addition, a comprehensive simulation study under various population scenarios is conducted to support and validate empirical findings.

Ranked set sampling is an alternative to simple random sampling, which uses the least amount of money and time. The ranked set sampling (RSS) is modified to obtain a more efficient and cost-effective estimator of population parameters. This paper aims to bring a more efficient and cost-effective design than stratified ranked set sampling and simple random sampling. In some distributions, the suggested method used fewer sample units than stratified ranked set sampling and gives a more efficient estimation of population parameters. In symmetric distributions, the proposed design, called "partial stratified ranked set sampling" yields an unbiased estimator of the population mean. The design is illustrated with practical data of COVID-19 confirmed cases.

In surveys when measuring units is expensive, ranked set sampling (RSS) is a popular and economical sampling technique. The RSS algorithm selected units using a ranking procedure. Either eye inspection or an auxiliary variable is used for ranking. In the present paper, ‘stratified dual-rank ranked set sampling’ (SDuRSS) method is suggested to estimate population mean. The proposed design used dual ranking instead of traditional ranking method. The mean and variance of the suggested scheme is derived. The performance of the mean estimator of proposed scheme is investigated by relative efficiency (RE) of the estimator. A simulation study is conducted for computing such relative efficiency which shows that the proposed design is more efficient than stratified ranked set sampling (SRSS) and stratified extreme ranked set sampling (SERSS). The proposed scheme is illustrated with real data set where it also shows superiority on the SRSS and SERSS.

Koyuncu and Kadilar <cite>kk.2009</cite> introduced a family of estimators under simple random sampling. In this article; we adapt these estimators for ranked set sampling. Further, we suggest a regression-type estimator of population mean utilizing available supplementary information under ranked set sampling scheme alongside the sensitivity issue when the variate of interest is sensitive. The bias and mean square error of the suggested estimator is determined theoretically for both situations. A simulation study has been done to demonstrate the percentage relative efficiency of proposed estimators over the adapted and reviewed estimators.

ABSTRACTIn this paper, ranked set sampling is proposed for constructing a non-parametric quality control chart based on sign statistic for monitoring the process center when the units are difficult and costly to measure. The characteristics of run length such as average, median and standard deviation are used as criteria to compare two sampling schemes: ranked set sampling and simple random sampling. Cauchy, double exponential and normal distributions are applied to investigate the performance of sign control chart based on studied sampling schemes. The proposed control chart is illustrated with a real data set. The results indicate that when the process starts to get out of control, the chart based on ranked set sampling reduces the run length characteristics values.

Weighted modified ranked set sampling methods