This paper investigates the concomitants of order statistics from the bivariate generalized linear exponential (BGLE) distribution. We obtain the probability density function of a single concomitant and the joint probability density function of two concomitants of order statistics from the BGLE distribution. In addition, expressions for the single and product moments of concomitants of order statistics are derived. Furthermore, we find the best linear unbiased estimator of a scale parameter related to a study variable using various ranked set sampling techniques. Finally, we apply the findings to a real-life dataset.

Statistical inference for the unit compound Rayleigh model under ranked set sampling with application

This research aims to demonstrate the high efficiency and accuracy in estimating the limited population mean through the estimates of the separate and combined stratified regression line based on the method of median ranked set sampling to choose a sample that is more representative of the community. With the problem of heterogeneity in the data and containing extreme values ​​(outliers), it is recommended to use stratification of the community and draw samples using the method of sampling the middle ordered from these layers, which is known as the stratified median ranked set sampling ( ), which is one of the modified ranked set sampling methods (RSS), where the mean square error (MSE) of the population mean estimator obtained in this way was compared with the MSE value of the population mean estimator obtained through regression estimates using the robust variance and covariance matrix (Minimum Covariance Determinant (MCD), Minimum Volume Ellipsoid (MVE)) to calculate the averages and using robust methods (Huber M, Huber MM, Least Median of Squares (LMS), Least Trimmed Squares (LTS)) to estimate the regression parameter. The simulation results show that the proposed estimator outperforms the robust estimators in most cases because it obtains the lowest values of the mean square error.

Abstract Ranked Set Sampling (RSS) serves as an effective and efficient alternative to Simple Random Sampling (SRS), especially when ranking items is easier than taking precise measurements. Stratified sampling is used for better estimation when the population is heterogeneous. In this work, we introduce a new family of nearly unbiased estimators for estimating the population mean under the RSS and SRSS framework. These estimators are formulated as linear combinations of three established estimators and are specifically developed to minimize bias to the first order. We analytically derive their theoretical properties, including bias and Mean Squared Error (MSE), to evaluate their statistical performance. To support our theoretical claims, we apply the proposed estimators to real-world data and perform extensive simulation experiments under varying sample sizes and correlation settings. We benchmark our estimator against existing ones such as the conventional sample mean, the exponential ratio estimator, and the logarithmic estimator. The assessment is based on key metrics like MSE and Percentage Relative Efficiency (PRE). The findings consistently show that the proposed estimator yields lower MSE and higher PRE, indicating better accuracy and efficiency under both sampling frames. Furthermore, its near-unbiased behaviour enhances its practical applicability, particularly in scenarios where ranking is more feasible than direct measurement.

Abstract This paper develops innovative estimators based on ranked set sampling (RSS) for estimating the population mean in the presence of non-response (NR) errors, utilizing auxiliary information. RSS is shown to be a more efficient alternative to simple random sampling (SRS), particularly under non-response conditions. The proposed estimators are evaluated against existing ratio, regression, and exponential estimators using bias, mean squared error (MSE), and percent relative efficiency (PRE). Results from empirical analysis and simulation studies demonstrate that the RSS-based estimators achieve lower MSE and higher PRE, thereby outperforming conventional methods. The study highlights the practical advantages of RSS in survey sampling and contributes to improving the robustness and accuracy of estimators under non-response error scenarios, while also suggesting directions for future research.

The sampling strategy has a considerable impact on the representativeness of the sampled data and can lead to incorrect estimates if not carefully chosen. An improved method over more conventional simple random sampling (SRS) is ranked set sampling (RSS). The RSS is more efficient, reducing the number of measurements needed for a desired level of precision, especially in challenging data collection scenarios. The Monsef distribution is a recent mixture lifetime model that has demonstrated effectiveness in modeling various real-world datasets. Several mathematical aspects of the Monsef distribution include quantiles, upper incomplete moments, lower incomplete moments, stochastic ordering, and extropy measures. This work investigates the use of RSS in conjunction with several traditional estimation techniques to estimate the parameters of the Monsef distribution. Fifteen different estimation procedures are investigated, including maximum product spacing, some minimum spacing distance methods, the Kolmogorov method, ordinary least squares, maximum likelihood, and weighted least squares. To assess the performance of the estimation techniques for a range of sample sizes under perfect ranking conditions and both sampling techniques, a simulation scenario is conducted. The partial and total ranks of numerous estimates are displayed to determine the best estimation approach. According to simulation results, the maximum likelihood and maximum product spacing approaches consistently outperform other methods in evaluating the estimated quality for both RSS and SRS. To demonstrate the feasibility of the different methods, three authentic datasets from various fields are examined.

Estimating the bivariate distribution parameter is crucial for modeling paired variable dependencies, but highly variable or resource-intensive data may not respond well to traditional simple random sampling (SRS). In order to maximize efficiency, Ranked Set Sampling (RSS) ranks a subset of observations based on a concurrent variable, hence selecting just a subset for measurement. This study use both Bayesian and non-Bayesian estimation techniques to estimate the parameters of the Bivariate Inverse Weibull (BIW) distribution under RSS and SRS. According to the Marshall-Olkin approach, dependencies are captured by the BIW model using the parameters. We compute the probability functions for RSS and SRS because the ranking technique and dependence structure are intricate. Based on SRS and RSS, Bayesian estimators are explicitly derived by applying conjugate gamma priors for model parameters under squared error loss, whereas Maximum Likelihood Estimation (MLE) solutions are derived numerically via the Newton-Raphson technique because of the likelihood equations' nonlinearity. Mean Squared Error (MSE), Bias, and Efficiency (EFF), simulations conducted with four different parameter settings that showed that RSS routinely performs better than SRS. In particular, under RSS, Bayesian estimation frequently produces lower MSE and bias than MLE. Nevertheless, prior decisions have an impact on Bayesian performance, particularly when the parameters are tiny, Simulations with 10,000 Monte Carlo replications across four parameter sets show that RSS consistently outperforms SRS, with MSE reduced by up to 50% and EFF exceeding 10 for large samples. Bayesian estimation with conjugate gamma priors yields lower MSE than MLE, particularly under RSS, though prior selection is critical for small parameters. We recommend RSS with Bayesian methods for applications in reliability and lifespan analysis, as demonstrated on a real dataset of 243 men's body fat and chest circumference.

When measuring a key variable is difficult or expensive, ranked set sampling provides an effective alternative for collecting data. This study investigates the estimation of parameters for the exponentiated inverted Weibull distribution using ranked set sampling and its specific forms, including extreme ranked set sampling and median ranked set sampling. Since the exponenti-ated inverted Weibull distribution is widely applied in the analysis of lifetime and reliability data, obtaining precise parameter estimates is essential for sound statistical inference. The research compares the maximum likelihood estimates of the distribution’s parameters under different sampling schemes, namely simple random sampling, ranked set sampling, extreme ranked set sampling, and median ranked set sampling. An extensive simulation study is conducted to assess the performanceof these estimation methods in terms of bias, mean squared error, and relative efficiency under a range of sampling conditions. The study shows that variations in the size of the set and sampling cycles influence the accuracy of the estimate, with ranked set sampling, especially its extreme and median forms, generally outperforming simple random sampling.

This research examines the parameter estimation in the Morgenstern-type bivariate exponentiated inverted Weibull distribution (MTBEIWD) utilizing an innovative sampling framework grounded in concomitant record ranked set sampling (CRRSS). The main aim is to obtain the best linear unbiased estimate (BLUE) for the population mean using the CRRSS method and to assess its efficacy relative to the estimate derived using concomitant record values (CRV). Explicit formulations for the BLUE, its variance, and associated coefficients are derived using both methodologies. A thorough simulation study is performed to evaluate the influence of correlation between auxiliary and primary variables, along with the effect of sample size. The findings indicate that the CRRSS-based BLUE constantly surpasses the CRV-based estimate in efficiency, especially under elevated correlations and bigger sample sizes. Graphical evaluations corroborate these findings, demonstrating enhanced stability and accuracy in the estimations derived by CRRSS. This study emphasizes the practical benefits of integrating auxiliary information and record-based sampling into the estimate process, providing a more efficient method for parameter inference in bivariate reliability and lifetime models.

ABSTRACT Estimation of stress‐strength reliability is an important research topic in engineering and statistics. Traditional methods predominantly rely on simple random sampling to estimate system reliability. However, in recent years, ranked set sampling has emerged as a cost‐effective and efficient alternative to simple random sampling. Despite its growing popularity, the application of ranked set sampling to stress‐strength reliability in discrete models has not been sufficiently explored. This study provides a detailed statistical analysis of stress‐strength reliability when stress and strength are modeled as independent discrete random variables with a Poisson transmuted record type exponential distribution. Both point estimates and bootstrap confidence intervals are used to derive stress‐strength reliability estimates under both simple random sampling and ranked set sampling frameworks. The effectiveness of the estimates is evaluated through extensive Monte Carlo simulations, comparing their performance in various settings. Furthermore, simulation results from the analysis of three datasets demonstrate that the ranked set sampling estimates generally outperform traditional simple random sampling estimates in terms of both efficiency and accuracy. These findings highlight the potential advantages of ranked set sampling for estimating system reliability and contribute significantly to the field by demonstrating the applicability of the method to discrete models. Particularly for small sample sizes, the ranked set sampling method provides more consistent and reliable estimates than simple random sampling, lower confidence intervals, and reduced estimation errors.

Non-response is one of the major issues frequently encountered in applied research, and it significantly impairs the reliable estimation of population parameters. In this study, regression estimators utilizing information from two auxiliary variables are proposed under Ranked Set Sampling and Median Ranked Set Sampling methods in the presence of non-response. A comprehensive simulation study was conducted to evaluate the efficiency of the proposed estimators. In addition, the applicability of these estimators was demonstrated through a real data application. Based on the evaluation results, the proposed estimators demonstrated higher efficiency than the conventional regression and ratio estimators.

In this paper, the ranked set sampling method (RSS) is considered for estimating the inverse power Lindley distribution (IPLD) parameters and compared with the commonly simple random sampling. Different estimation methods are investigated including the commonly maximum likelihood, minimum distance estimation methods (Anderson Darling (AD), right tail Anderson Darling, left tail Anderson Darling, AD left tail second order, Cramér-von Mises), methods of maximum and minimum spacing distance (maximum product spacing distance, minimum spacing distance), methods of ordinary and weighted least squares, and the Kolmogorov–Smirnov method. A simulation study is conducted to compare these methods using RSS and SRS based on the same number of measured units in terms of mean squared error, bias, efficiency, and mean relative estimation error. A failure data set is fitted to the IPLD and the proposed estimation methods are applied to the data.

Small area estimation under ranked set sampling: simulation and real life application with crop production data

In this paper, we explore the maximum likelihood estimator (MLE) for the location parameter. Our primary emphasis is on the application of median ranked set sampling (MRSS) and we examine its characteristics regarding large sample sizes with application to asymptotic confidence interval (ACI). We demonstrate both the existence and uniqueness of the MLE of the location parameter for the normal distribution and extreme value distribution when MRSS is applied. Based on numerical results of the two distributions, MRSS produces the ACIs with shorter lengths and coverage probability closer to the nominal level compared to both SRS and RSS. Additionally, we compare the lengths and coverage probability of the ACIs under MRSS with imperfect ranking to those under SRS, as well as to those under RSS with imperfect ranking, for the two distributions.

Kolmogorov–Smirnov test under dependent and independent ranked set sampling based on single and double stage designs

Minimum ranked set sampling offers an effective approach for collecting failure time data while optimizing testing resources. This paper examines dependent competing risks model within the context of m-cycle minimum ranked set sampling data. Assuming that component lifetimes adhere to a two-parameter generalized inverted exponential distribution, we develop dependence structures utilizing the Marshall-Olkin distribution framework. The study establishes maximum likelihood estimation and Bayesian inference procedures under both unrestricted parameters and ordered restrictions. The theoretical analysis confirms the existence and uniqueness conditions for maximum likelihood estimators, with corresponding interval estimators being subsequently derived. For Bayesian inference, we derive posterior estimates under flexible prior specifications, employing Metropolis-Hastings and importance sampling algorithms to address complex posterior calculations. Through comprehensive numerical simulations and real-world case analysis, this study systematically evaluates the comparative performance of different estimation approaches while examining how cyclic sampling strategies influence estimation precision. Finally, implementation guidelines and production-oriented conclusions are provided based on the study results.

Estimation of the common location parameter of several distributions when their common scale parameter is proportional to with known coefficient of variation by ranked set sampling

Control charts may aid in maintaining and improving the efficiency of manufacturing and industrial processes. Nonparametric control charts are more dependable and practical than parametric charts when it is unclear how the data will be distributed. Also, when the distribution of the underlying process is unknown or uncertain, nonparametric control charts are required. The nonparametric charts are a reliable alternative that also can quickly detect shifts in process parameter(s). For effective process location monitoring, we have developed a nonparametric extended exponentially weighted moving average chart based on the Wilcoxon signed rank test under ranked set sampling(hereafter named REEWMAWSR). The performance of the proposed REEWMAWSR chart has been evaluated by calculating the run-length properties using the Monte Carlo simulations approach. The in-control and out-of-control run-length profiles of the proposed chart are also investigated under normal, non-normal, and contaminated normal distributions. Performance comparison of the proposed REEWMAWSR chart is done with various usual and nonparametric charts. The proposed chart's practical implementation is also illustrated using a real-life application.

Introduction This study introduces a novel HEWMA-based memory-type exponential estimator for Ranked Set Sampling (RSS). The proposed estimator combines HEWMA control chart statistics with the exponential ratio estimator to enhance efficiency. By incorporating control chart statistics, memory-type estimators improve estimation accuracy by using both the current sample's mean and past mean(s), if available. This method is particularly beneficial for time-dependent repeated survey data or data collected from the same population at different time points. Material and Methods The proposed estimator's performance is evaluated through simulation studies using synthetic datasets, which simulate various scenarios with different correlation coefficients. An empirical study is also conducted using real-world data with a distinct structure. The evaluation focuses on the estimator's efficiency, considering factors such as sample size, correlation, and the number of past means incorporated. Results The simulation results demonstrate that incorporating at least one past sample mean value significantly enhances efficiency. Moreover, the estimator's effectiveness improves as both the correlation between samples and the number of old means (T) increase. The weight parameters of the HEWMA estimator play a critical role in determining its performance, with optimal results observed at low to medium correlation levels. The estimator consistently outperforms the existing alternatives in the real data analysis. Discussion The proposed HEWMA-based memory-type exponential estimator offers a more efficient alternative to the EWMA-type ratio estimator in the RSS method. The findings highlight the importance of selecting appropriate HEWMA weight parameters based on sample size and correlation. This approach substantially improves estimation accuracy, especially in time-dependent and longitudinal data scenarios. The proposed estimator performs particularly well under low to medium correlation conditions, and its applicability to real-world data further supports its practical utility.

In the manufacturing industry, control charts are essential statistical tools for efficient process monitoring. Statistical process monitoring typically focuses on two main concerns: the location and variability of the quality characteristic of interest. While location monitoring is important, the monitoring of process dispersion has remained a significant area of research. The Shewhart S 2 chart is one of the most widely used tools for monitoring process dispersion. In this study, we evaluate the performance of the S 2 control chart when the unknown parameter is estimated from Phase I sample. Different proportion of outliers is contaminated into Phase I sample, which results in elevated average ARL . Although conventional simple random sampling ( SRS ) is commonly used, ranked set sampling ( RSS ) schemes have proven to be more effective in estimating process parameters. This study aims to design robust S 2 charts utilizing various outlier detectors under different RSS schemes. Specifically, we considered RSS and Folded Ranked Set Sampling ( FRSS ) schemes for establishing detection limits, so that the elevation caused by the outliers can be controlled. The performance is assessed using metrics such as the Average ARL and the standard deviation of ARL . To illustrate the proposed procedures, we apply them to industrial data for demonstrating their effectiveness.