Ranked Set Sampling Research Articles

Adaptive Exponentially Weighted Moving Average Control Chart for Monitoring Process Mean Under Ranked Set Sampling Schemes

Adaptive Exponentially Weighted Moving Average Control Chart for Monitoring Process Mean Under Ranked Set Sampling Schemes

Correction to: Log-logistic parameters estimation using moving extremes ranked set sampling design

Correction to: Log-logistic parameters estimation using moving extremes ranked set sampling design

Parametric estimation for the simple linear regression model under moving extremes ranked set sampling design

Parametric estimation for the simple linear regression model under moving extremes ranked set sampling design

A Two-Parameter Model: Properties and Estimation under Ranked Sampling

This study introduces a flexible model with two parameters by combining the type II half-logistic-G family with the inverted Topp–Leone distribution. The proposed model is referred to as the half logistic inverted Topp–Leone (HLITL) distribution. The associated probability density function can be considered a mixture of the inverted Topp–Leone distributions. The proposed model can be deemed an acceptable model for fitting the right-skewed, reversed J-shaped, and unimodal data. The statistical properties, including the moments, Bonferroni and Lorenz curves, Rényi entropy, and quantile function, are derived. Additionally, the plots of the skewness and kurtosis measures are plotted based on the quantiles. The parameter estimators are implemented using the maximum likelihood method based on two sampling schemes: the simple random sample method and the ranked set sampling method. The proposed method is evaluated by using simulations. The results show that the maximum likelihood estimates of the parameters under ranked set sampling are more accurate than those under simple random sampling. Generally, there is good agreement between the theoretical and empirical results. Two real datasets are used to compare the HLITL model with the following models: alpha power exponential, alpha power Lindley, odd Fréchet inverse exponential, and odd Fréchet inverse Rayleigh models. The comparison results show that the HLITL model represents a better alternative lifetime distribution than the other competitive distributions.

Sequential procedures for two-sample problem based on early failures from ranked set samples

In this article, a class of sequential precedence tests based on ranked set samples (RSS-SPT) with different sequential rank schemes and different α-spending is proposed. The exact null distributions of the proposed RSS-SPT test statistics are derived and the corresponding critical values are tabulated. The performance of the class of RSS-SPT is evaluated in terms of their the power values and their efficiencies by means of the expected stopping location, expected number of failures, and expected total experimental time consumed. The exact power functions and efficiencies of different test procedures under the Lehmann alternative are derived. The performance of RSS-SPT is compared with the nonsequential precedence test based on ranked set samples under the Lehmann alternative based on exact calculation and under the location-shift alternative using Monte Carlo simulations. Conclusions and recommendations are provided based on the numerical results.

New estimator for the variances of strata in ranked set sampling

New estimator for the variances of strata in ranked set sampling

Memory type ratio and product estimators under ranked-based sampling schemes

The exponential weighted moving average (EWMA) statistic is utilized the past information along with the present to enhance the efficiency of the estimators used for estimating the population parameters. In this study, the EWMA statistic is used for the estimation of population mean with suitable auxiliary information. The memory type ratio and product estimators are proposed under ranked-based sampling (RBS) schemes including extreme ranked set sampling, median ranked set sampling, and quartile ranked set sampling. The expressions of mean square errors (MSE) of the proposed estimators are derived. An extensive simulation study is conducted to evaluate the performance of the proposed estimators. An empirical study is presented based on real-life data that supports the findings of the simulation study.

A New Application of Generalized Linear Failure Rate Distribution in Agriculture Using Ranked Set Sampling

Abstract This article deals with perform inferences about stress–strength model R=P[Y<X] when X and Y are two independent random variables with generalized linear failure rate distribution (GLFRD) with the same and known scale parameters but not identically shaped parameters. In the literature, estimators based on simple random sample (SRS) are widely used in estimating stress–strength model. But in the resent years, ranked set sampling (RSS) has become popular in performing statistical inference. Therefore, the estimator of R based on RSS using maximum likelihood and modified maximum likelihood are obtained. Monte Carlo simulation study is performed to compare the estimators of R are obtained using RSS and SRS. Finally, agriculture application is presented.

Mean ranked acceptance sampling plan under exponential distribution

Abstract This study proposes a new acceptance sampling scheme, namely mean ranked sampling scheme, for efficient decision of statistical quality control. The proposed scheme is based on ranked set sampling under exponential distribution for acceptance or rejection of a lot. Two-point method on operating characteristic function is used for the derivation of plan parameters assuming approximation of exponential to normal distribution. The minimum sample sizes and acceptance numbers are obtained satisfying producer’s and consumer’s risk at certain levels of acceptable (AQL) and tolerable quality (RQL). The main advantages of proposed scheme are (i) data is selected by using free cost sampling method from a large lot and (ii) all units of selected lot are used in making decision. The probability & distribution functions for proposed mean ranked set sampling plan are derived. The OC values comparison with simple random sampling is presented. It is shown that the tables presented here can be used if mean life of units are chosen as a criterion.

Bayesian Estimation and Prediction of the Rayleigh Distribution Based on Ordered Ranked Set Sampling under Type-II Doubly Censored Samples

Bayesian Estimation and Prediction of the Rayleigh Distribution Based on Ordered Ranked Set Sampling under Type-II Doubly Censored Samples

Cumulative residual extropy of minimum ranked set sampling with unequal samples

Recently, an alternative measure of uncertainty called cumulative residual extropy (CREX) was proposed by Jahanshahi et al. (2019). In this paper, we consider uncertainty measures of minimum ranked set sampling procedure with unequal samples (MinRSSU) in terms of CREX and its dynamic version and we compare the uncertainty and information content of CREX based on MinRSSU and simple random sampling (SRS) designs. Also, using simulation, we study new estimators of CREX for MinRSSU and SRS designs in terms of bias and mean square error. Finally, we provide a new discrimination measure of disparity between the distribution of MinRSSU and parental data SRS.

A new application of R = P[Y < X] for the inverse Lindley distribution using ranked set sampling

In this paper, we consider the problem of performing inference about reliability parameter R = P[Y < X] based on ranked set sampling (RSS) when the distribution of stress Y and strength X are inverse Lindley. The point estimator of R based on (RSS) using maximum likelihood method is obtained. In context of interval estimation an asymptotic confidence interval (ACI) and bootstrap confidence interval (BCI) are derived for R based on (RSS). The effectiveness of the proposed estimator is indicated in simulation study which compare the proposed estimators by their corresponding based on simple random sample (SRS). Finally a real data in medicine is used to illustrate our proposed estimators.

On developing sensitive nonparametric mixed control charts with application to manufacturing industry

AbstractControl charts are designed under the normality assumption of the quality characteristic of the process. However, the normality assumption rarely holds in practice. In non‐normal conditions, parametric charts tend to display more false alarm rates and invalid out‐of‐control comparisons. The exponentially weighted moving average chart is a frequently used memory‐type control chart for monitoring the process target that only performs effectively under the smoothing parameter's small choices. This study proposes a nonparametric mixed exponentially weighted moving average‐progressive mean chart based on sign statistic (NPMEPSN) under simple and ranked set sampling schemes to address this said drawback. Normal and non‐normal distributions are included in this study to observe the proposed chart's in‐control behavior and out‐of‐control efficacy. The prominent feature of the proposed schemes is that it works efficiently in detecting small and persistent shifts in the process location corresponding to the given values of the smoothing parameter. The proposed scheme is also tested under the ranked set sampling scheme to enhance the NPMEPSN chart's performance (hereafter named “NPMEPRSN”). The performance of the proposed charts is investigated through simulations using run‐length profiles. The proposed schemes were seen to outperform other alternatives, specifically under the ranked set sampling scheme. A real data‐set related to the diameter of a piston ring is included as a demonstration of the proposal.

Efficient Estimation of a Scale Parameter of Bivariate Lomax Distribution by Ranked Set Sampling

Ranked set sampling (RSS) is an efficient technique for estimating parameters and is applicable whenever ranking on a set of sampling units can be done easily by a judgment method or based on an auxiliary variable. In this paper, we assume [Formula: see text]to have bivariate Lomax distribution where a study variable [Formula: see text]is difficult and/or expensive to measure and is correlated with an auxiliary variable [Formula: see text] which is readily measurable. The auxiliary variable is used to rank the sampling units. In this article, we propose an estimator for the scale parameter of bivariate Lomax distribution using some of the modified RSS schemes. Efficiency comparison of the proposed estimators is performed numerically as well as graphically. A simulation study is also performed to demonstrate the performance of the proposed estimators. Finally, we implement the results to real-life datasets. AMS classification codes: 62D05, 62F07, 62G30

Estimating the Reliability of a Component between Two Stresses from Gompertz-Frechet Model

In this paper, the reliability of the stress-strength model is derived for probability P( &lt;X&lt; ) of a component strength X between two stresses , , when X and , are independent Gompertz Fréchet distribution with unknown and known shape parameters and common known scale parameters. Different methods used to estimate R and Gompertz Fréchet distribution parameters which are [Maximum Likelihood, Least square, Weighted Least square, Regression and Ranked set sampling methods], and the comparison between these estimations by simulation study based on mean square error criteria. The comparison confirms that the performance of the maximum likelihood estimator works better than the other estimators.

English

We propose a new exponential type estimator for the population mean by adapting the estimator suggested by Kadilar [12] to the Ranked Set Sampling (RSS). Theoretically and numerically, we show that the proposed exponential type estimator is more efficient than the classical ratio estimator in the RSS and the estimator of Kadilar et al. [11].

Fisher Information in Moving Extreme Ranked Set Sampling with Application to Parameter Estimation

In statistical parameter estimation problems, how well the parameters are estimated largely depends on the sampling design used. In the current paper, a modification of ranked set sampling called moving extremes ranked set sampling (MERSS) is considered for the Fisher information matrix for the location-scale family. The Fisher information matrix for this model are respectively derived under simple random sampling and MERSS. In order to give more insight into the performance of MERSS with respect to simple random sampling, the Fisher information matrix for usual location-scale distributions are respectively computed under the two sampling. The numerical results show that MERSS provides more information than simple random sampling in parametric inference.

Estimation of a Scale Parameter of Morgenstern Type Bivariate Uniform Distribution by Ranked Set Sampling

In this paper, we obtain several estimators of a scale parameter of Morgenstern type bivariate uniform distribution (MTBUD) based on the observations made on the units of the ranked set sampling regarding the study variable Y which is correlated with the auxiliary variable X, when (X;Y ) follows a MTBUD. Eciency comparisons among these estimators are also made in this work. Finally, we illustrate the methods developed by using a real data set.

Ranked set sampling with lowest order statistics for Pareto distribution

Ranked set sampling (RSS) is a method of sampling that can be advantageous when quantification of all sampling units is costly but when small sets of units can be ranked according to the character under investigation by means of visual inspection or other methods not requiring actual measurements. RSS performs better than simple random sampling (SRS) to estimate the population mean. In original RSS procedure, the units corresponding to each rank are used. In this article, we propose to use RSS method with lowest order statistics from each sample to estimate the population mean of Pareto distribution which is highly positively skew. The Pareto distribution is chosen due to its application in social and scientific phenomenon including the distribution of wealth in a society. The estimator based on lowest order statistics with bias correction term has been proposed. Two cases, known and unknown scale parameter, have been considered. The simulation-based methods have also been included. It is shown that the gains in the relative precisions of population mean based on our proposed method are uniformly higher than those based upon the RSS and extreme RSS procedures. The proposed method with bias correction term is recommended for real applications.

Some Shrinkage estimators based on median ranked set sampling

In this study, some shrinkage estimators using a median ranked set sample in the presence of multicollinearity were studied. Initially, we constructed the multiple regression model using median ranked set sampling. We also adapted the Ridge and Liu-type estimators to these multiple regression model. To investigate the efficiency of these estimators, a simulation study was performed for a different number of explanatory variables, sample sizes, correlation coefficients, and error variances in perfect and imperfect ranking cases. In addition, these estimators were compared with other estimators that are based on ranked set sample using simulation study. It is shown that when the collinearity is moderate, Ridge estimator using median ranked set sample performs better than other estimators and when the collinearity increases, Liu-type estimator using median ranked set sample gets better than all other estimators do. When the collinearity is smaller than 0.95, ridge estimator based on median ranked set sample is more efficient than Liu-type estimator based on same sample. However, this threshold increases as the sample size increases and the number of explanatory variables decreases. In addition, real data example is presented to illustrate how collinearity affects the estimators under median ranked set sampling and ranked set sampling.