Ranked Set Sampling Research Articles

Monitoring of manufacturing process using bayesian EWMA control chart under ranked based sampling designs

Control charts, including exponentially moving average (EWMA) , are valuable for efficiently detecting small to moderate shifts. This study introduces a Bayesian EWMA control chart that employs ranked set sampling (RSS) with known prior information and two distinct loss functions (LFs), the Square Error Loss function (SELF) and the Linex Loss function (LLF), for posterior and posterior predictive distributions. The chart's performance is assessed using average run length (ARL) and standard deviation of run length (SDRL) profiles, and it is compared to the Bayesian EWMA control chart based on simple random sampling (SRS). The results indicate that the proposed control chart detects small to moderate shifts more effectively. The application in semiconductor manufacturing provides concrete evidence that the Bayesian EWMA control chart, when implemented with RSS schemes, demonstrates a higher degree of sensitivity in detecting deviations from normal process behavior. Comparison to the Bayesian EWMA control chart using SRS, it exhibits a superior ability to identify and flag instances where the manufacturing process is going out of control. This heightened sensitivity is critical for promptly addressing and rectifying issues, which ultimately contributes to improved quality control in semiconductor production.

Enhancing mean estimators in median ranked set sampling with dual auxiliary information

When measuring the research variable is complicated, expensive, or problematic, median ranked set sampling (MRSS) is often utilized since it is straightforward to rank the components using a low-cost sorting criterion. Using this sampling scheme, many authors considered the problem of population mean estimation with a single auxiliary variable in order to obtain more precised estimators than the traditional ratio type regression estimators. In this article, we extend their ideas based on regression approach using two auxiliary variables and introduce a new regression-type estimator along with its theoretical expression of minimum mean square error (MSE). The suggested estimator's applicability is demonstrated using both simulated and real-world data sets.

Adaptive EWMA control chart for monitoring the coefficient of variation under ranked set sampling schemes

In this study, we introduce an Adaptive Exponentially Weighted Moving based Coefficient of Variation (AEWMCV) control chart, designed to address situations where the process mean fluctuates over time and the standard deviation of the process changes linearly with the process mean. To enhance the efficiency and effectiveness of the control chart, we integrate the ranked set sampling method and its modified schemes, such as Simple Random Sampling, Quartile RSS, Median RSS, and Extreme RSS. The performance of the proposed AEWMCV control chart and the studied CV control charts are evaluated using the Average Run Length and Standard Deviation of Run Length metrics. Our findings reveal that the proposed control chart outperforms the existing CV control charts, especially in detecting slight to moderate changes in the process CV. To illustrate the practical applicability of the suggested control chart, we present an example demonstrating its use on a real dataset. The results highlight the superior performance of the AEWMCV control chart in accurately detecting and responding to changes in the process CV. In conclusion, our study introduces an innovative AEWMCV control chart that combines ranked set sampling and its modified schemes to enhance performance in scenarios with fluctuating process means and changing standard deviations. The proposed control chart proves to be more effective in detecting subtle variations in the process CV compared to traditional CV control charts. This research provides a valuable contribution to the field of control chart methodology, especially when dealing with challenging or costly data collection scenarios.

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 common mean of two normal distributions using ranked set sampling and some of its variations

The estimation of the common mean of two normal distributions based on ranked set sampling (RSS) techniques is considered. In particular, RSS, moving extreme ranked set sampling, median ranked set sampling, and steady-state ranked set sampling are used. The estimators obtained are compared with each other and with their counterparts using simple random sampling (SRS). Allocation of sample size between the two distributions is considered using Neyman allocation. It turned out that the suggested estimators are more efficient than their counterparts using SRS.

A novel proposed class of estimators under ranked set sampling: Simulation and diverse applications

This study presents a novel enhanced exponential class of estimators for population mean under RSS by employing data on an auxiliary variable. The suggested estimators' mean square error (MSE) is calculated approximately at order one. The efficiency conditions that make the suggested enhanced exponential class of estimators superior to the traditional estimators are found. A simulation study using hypothetically drawn normal and exponential populations evaluates the execution of the suggested estimators. The findings demonstrate that the suggested estimators outperform their traditional equivalents. In addition, real data examples are examined to show how the proposed estimators can be implemented in various real life problems.

VARIANCE ESTIMATORS USING NON-PARAMETRIC APPROACH UNDER DIFFERENT RANKED SET SAMPLING SCHEMES

Estimation of variance is a commonly discussed topic under simple random sampling (SRS) scheme. The current article deals the issue of variance estimation utilizing supplementary information with the nonparametric approach under different ranked set sampling (RSS) schemes. We propose a class of nonparametric variance estimators utilizing kernel regression [1] with different bandwidths (Plug-in and Cross-validation), under RSS schemes. Simulation study is provided utilizing diverse data sets. The comparison of simulation results has been made between the members of the proposed class with respect to the unbiased variance estimator.

Integration of Bayesian Adaptive Exponentially Weighted Moving Average Control Chart and Paired Ranked-Based Sampling for Enhanced Semiconductor Manufacturing Process Monitoring

Exponentially weighted moving average (EWMA) and Shewhart control charts are commonly utilized to detect the small to moderate and large shifts in the process mean, respectively. This article introduces a novel Bayesian AEWMA control chart that employs various loss functions (LFs), including square error loss function (SELF) and LINEX loss function (LLF). The control chart incorporates an informative prior for posterior and posterior predictive distributions. Additionally, the control chart utilizes various paired ranked set sampling (PRSS) schemes to improve its accuracy and effectiveness. The average run length (ARL) and standard deviation of run length (SDRL) are used to evaluate the performance of the suggested control chart. Monte Carlo simulations are conducted to compare the performance of the proposed approach to other control charts. The results show that the proposed method outperforms in identifying out-of-control signals, particularly under PRSS schemes compared to simple random sampling (SRS). The proposed CCs effectiveness was validated using a real-life semiconductor manufacturing application, utilizing different PRSS schemes. The performance of the Bayesian AEWMA CC was evaluated, demonstrating its superiority in detecting out-of-control signs compared to existing CCs. This study introduces an innovative method incorporating various LFs and PRSS schemes, providing an enhanced and efficient approach for identifying shifts in the process mean.

A Novel Sub-Type Mean Estimator for Ranked Set Sampling with Dual Auxiliary Variables

This research introduces a novel sub-estimator designed to estimate the population mean under ranked set sampling, motivated by the new concept of a recently introduced sub-ratio estimator. The mathematical formulas of the proposed estimator’s mean square error and bias are presented and theoretically contrasted with an analogous estimator found in the existing best sub-estimator literature. In addition to the theoretical analysis, empirical evidence is provided to validate the superiority of the proposed estimator. This empirical validation is based on numerical computations using Monte Carlo simulations, encompassing synthetic and real data applications. The results underscore the effectiveness of the proposed estimator. Finally, this study discusses the need for further research.

Optimal estimators of the population mean of a skewed distribution using auxiliary variables in median ranked-set sampling

ABSTRACT In an asymmetric population, individuals are concentrated toward one tail of the distribution. An estimator of the population mean in this asymmetric case is constructed on the basis of median ranked-set sampling, that is, the population is divided into subsets of equal size and the intersections of these sets depend on the chosen order of ranking according to a known auxiliary variable. Ranking individuals according to this auxiliary variable should approximate their ranking with respect to the unknown variable of interest. This procedure is a cost-effective way of selecting the sample when the variable of interest is unknown. To do this, the auxiliary variable must be at least weakly correlated with the variable of interest. The proposed estimator extends that constructed with extreme ranked-set sampling, whose principle is to divide the population into subsets whose intersections depend on the extreme values of the auxiliary variable. The mean square error of the estimator is expressed analytically. A simulation allows for comparing the proposed estimator with estimators based on simple random sampling and with those based on sampling sets of extreme values. A simulation shows that when the response variable is correlated with both auxiliary variables, even if these correlations are weak, around 0.5 in absolute value, then the mean square error of the proposed estimator is at least 175% lower than the mean square error of estimators based either on simple random or on extreme ranked-set samplings. A first application focuses on household incomes in the Iranian provinces of Fars and Khuzestan in 2022, first with the single gross income, which is the total income that an individual or household earns before tax as auxiliary variable and then with the two auxiliary variables of total gross household income and wages paid year-round to heads of households through the banking network. In this application, the mean square error of the proposed estimator with median ranked-set sampling is at least 60% lower than that obtained with simple random and extreme ranked-set samplings. In the application of the physical preparation score with runners’ track records as an auxiliary variable concerning 160 Iranian athletes in 2022 with sample sizes of 6, 8, 10, 25, and 30, the mean square error of the proposed estimator with median ranked-set sampling is at least 50% lower than that obtained with simple random and extreme ranked-set samplings. In the third application of the COVID-19 mean mortality rate in 2022 in the USA, Iran, Turkey, and Germany, with sample sizes of 6, 8, 10, 25, and 30, estimations of the mean mortality rate are based on new cases. In each of the four countries, the mean square error of the proposed estimator under median ranked-set sampling is at least 60% lower than that obtained with simple random and extreme ranked-set samplings.

Different classical estimation methods using ranked set sampling and data analysis for the inverse power Cauchy distribution

A recent two-parameter distribution that offers additional flexibility in modeling a real lifetime dataset is the inverse power Cauchy distribution (IPCD). The IPCD is user-friendly and analytically attractive, and it can be effectively utilized to analyze actual datasets. On the other hand, ranked set sampling (RSS) is a method of gathering data that first combines simple random sampling (SRS) with the expertise and judgment of the field investigator in determining where to take samples. The RSS is known to be more efficient than the SRS as well as less expensive since fewer sample units need to be procured and evaluated. In this article, various estimation techniques for IPCD are examined. The parameter estimates are determined utilizing the RSS and SRS of seven frequentist approaches, which are the maximum likelihood, Anderson-Darling, least squares, Cramér-von Mises, maximum product spacing, weighted least squares, and right-tail Anderson-Darling approaches. Using accuracy criteria, a simulation analysis is done to assess the efficacy of the provided RSS-based estimates. For further clarification, one real data analysis is provided.

Novel Logarithmic Imputation Methods Under Ranked Set Sampling

ABSTRACT The data we encounter in real life often contain missing values. In sampling methods, missing value imputation is done with different methods. This article proposes novel logarithmic type imputation methods for estimating the population mean in the presence of missing data under ranked set sampling (RSS). According to the determined theoretical results, the proposed imputation methods are found to be the most efficient in comparison to popularly known imputation methods like mean imputation, Al-Omari and Bouza (2014) imputation methods, Sohail et al. (2018) imputation methods, and Bhushan and Pandey (2016) type imputation methods utilizing RSS. Apart from this, a simulation study has been accomplished utilizing artificially drawn symmetric and asymmetric populations. The outcomes are encountered to be rather satisfactory, showing improvement over all existing imputation methods.

Performance of Bayesian EWMA control chart with measurement error under ranked set sampling schemes with application in industrial engineering

The objective of this study is to investigate the behavior of the Bayesian exponentially weighted moving average (EWMA) control chart in the presence of measurement error (ME). It explores the impact of different ranked set sampling designs and loss functions on the performance of the control chart when ME is present. The analysis incorporates a covariate model, multiple measurement methods, and a conjugate prior to account for ME. The performance evaluation of the proposed Bayesian EWMA control chart with ME includes metrics such as average run length and standard deviation of run lengths. The findings, obtained through Monte Carlo simulation and real data application, indicated that ME significantly affects the performance of the Bayesian EWMA control chart when RSS schemes are employed. Particularly noteworthy is the superior performance of the median RSS scheme compared to the other two schemes in the presence of ME.

Optimizing Mean Estimators with Calibrated Minimum Covariance Determinant in Median Ranked Set Sampling

Calibration methods enhance estimates by modifying the initial design weights, for which supplementary information is exploited. This paper first proposes a generalized class of minimum-covariance-determinant (MCD)-based calibration estimators and then presents a novel class of MCD-based calibrated estimators under a stratified median-ranked-set-sampling (MRSS) design. Further, we also present a double MRSS version of generalized and novel classes of estimators. To assess and compare the performance of the generalized and novel classes of estimators, both real and artificial datasets are utilized. In the presented practical scenarios and real-world applications, we utilize information from a dataset comprising 800 individuals in Turkey from 2014. These data include body mass index (BMI) as the primary variable of interest and age values as auxiliary variables. The BMI results shows that the proposed estimators (y¯PMI=581.1897,y¯PaMI=544.8397) have minimum and (y¯PMII=669.1822,y¯PaMII=648.2363) have maximum PREs in the case of single and double MRSS for odd sample sizes. Similarly, (y¯PMI=860.0099,y¯PaMI=844.7803) have minimum and (y¯PMII=974.5859,y¯PaMII=953.7233) have maximum PREs in the case of single and double MRSS for even sample sizes. Additionally, we conduct a simulation study using a symmetric dataset.

An extended exponential model: Estimation using ranked set sampling with applications

In this paper, we emphasize a new three-parameter lifetime distribution. It can be presented as a tractable complementary exponentiated Bell exponential distribution defined as a paragon of the complementary exponentiated Bell-generated family of distributions. In the first part, some essential properties of the proposed distribution, such as the quantile function, the linear representation of the probability density function, and the moment measures, are presented. The second part is focused on the model's applications in diverse statistical scenarios. In the first scenario, two sampling schemes, namely ranked set sampling and simple random sampling, are used to estimate the unknown parameters. A simulation study is provided to assess the performance of the estimates using the two sampling schemes, and their relative efficiencies are computed. In the second scenario, a group acceptance sampling plan for truncated life tests is elaborated. Finally, real data sets are considered to illustrate the practical interest of the findings.

Predictive estimation for mean under median ranked set sampling: an application to COVID-19 data

Predictive estimation for mean under median ranked set sampling: an application to COVID-19 data

Different estimation methods for the generalized unit half-logistic geometric distribution: Using ranked set sampling

The generalized unit half-logistic geometric distribution (GUHLGD) is a modern two-parameter unit distribution with attractive shape flexibility for the corresponding probability density and hazard rate functions. Due to its versatility, it may be used to model a variety of current bounded real-world datasets. On the other hand, an effective sampling strategy for both parametric and non-parametric inferences is the ranked set sampling (RSS) method. This article focuses on estimating the parameters of the GUHLGD based on the RSS method as well as the simple random sampling (SRS) method. Eleven traditional estimation methods are taken into consideration, including the percentile, Cramér–von Mises, maximum likelihood, Anderson–Darling, right-tailed Anderson–Darling, left-tailed Anderson–Darling, least squares, weighted least squares, minimum spacing absolute-log distance, maximum product of spacing, and minimum spacing absolute distance methods. A Monte Carlo simulation is employed to compare the performance of the resultant estimates based on some accuracy measures. We draw the conclusion that, for both sampling procedures, the maximum likelihood estimation methodology is the best option among the rest based on the partial and total ranking measures. The estimates based on the RSS method are more efficient than the others based on the SRS method. Results from actual data further support the advantage of the RSS design over the SRS design.

Bayesian and Non-Bayesian Estimation for a New Extension of Power Topp–Leone Distribution under Ranked Set Sampling with Applications

In this article, we intend to introduce and study a new two-parameter distribution as a new extension of the power Topp–Leone (PTL) distribution called the Kavya–Manoharan PTL (KMPTL) distribution. Several mathematical and statistical features of the KMPTL distribution, such as the quantile function, moments, generating function, and incomplete moments, are calculated. Some measures of entropy are investigated. The cumulative residual Rényi entropy (CRRE) is calculated. To estimate the parameters of the KMPTL distribution, both maximum likelihood and Bayesian estimation methods are used under simple random sample (SRS) and ranked set sampling (RSS). The simulation study was performed to be able to verify the model parameters of the KMPTL distribution using SRS and RSS to demonstrate that RSS is more efficient than SRS. We demonstrated that the KMPTL distribution has more flexibility than the PTL distribution and the other nine competitive statistical distributions: PTL, unit-Gompertz, unit-Lindley, Topp–Leone, unit generalized log Burr XII, unit exponential Pareto, Kumaraswamy, beta, Marshall-Olkin Kumaraswamy distributions employing two real-world datasets.

Some Improved Combined Estimators of Population Mean in Stratified Ranked Set Sampling

This paper presents improved population mean estimators using auxiliary variables in Stratified Ranked Set Sampling. We have derived the expressions for bias and mean square errors up to the first order of approximation and shown that the proposed estimators under optimum conditions are more efficient than other estimators taken in this paper. In an attempt to verify the efficiencies of proposed estimators, theoretical results are supported by numerical illustrations and simulation study for which we have considered two populations.

Computing the population mean on the use of auxiliary information under ranked set sampling

Computing the population mean on the use of auxiliary information under ranked set sampling