In this paper, we have proposed an estimator of finite population mean in stratified random Sampling. The expressions for the bias and mean square error of the proposed estimator are obtained up to the first order of approximation. It is found that the proposed estimator is more efficient than the traditional mean, ratio, exponential, regression, Shabbir and Gupta (in Commun Stat Theory Method 40: 199– 212, 2011) and Khan et al. (in Pak J Stat 31: 353– 362, 2015) estimators. We have utilized four natural and four artificial data sets Under stratified random Sampling scheme for assessing the performance of all the estimators considered here.

In this research, lifetime performance index (LPI) data are used to present a quick switching Sampling (QSS) plan based on a type‐II censoring life test and the assumption that the lifetime of units follows the Weibull distribution. In this proposed QSS plan, it is also assumed that the sample size (n) and the acceptance criterion (k) are the same for both the normal and the tightened inspections of the QSS plan, but the failures (r) during the normal and tightened inspections are different in number. The equations needed to calculate the operating characteristic (OC) curve are presented for the proposed QSS along with an optimization model to minimize the average failure number (AFN). In this regard, the constraints of producer and consumers' risks are incorporated into the model. To show the performance of the proposed QSS plan, numerical analyses are performed and the studies conducted in this field are compared. The introduced QSS Sampling plan can significantly reduce the cost of manufacturers at the level of industrial organizations.

Acceptance of Sampling plans and trade credit has become increasingly common in today's business. These two issues should be considered simultaneously when determining an ordering decision. This paper uses EOQ to model the decision Under the acceptance Sampling plan and trade credit; meaning, how often it would be necessary to order to minimize the total related cost. We develop theorems based on optimum lemmas to solve the problem. Computational analyses are given to illustrate the solution procedures and we discuss the inuence of credit period, acceptance Sampling plan, holding cost and ordering cost on the total cost, and the ordering decision. We conclude with a computational analysis that leads to a variety of managerial insights.

Auxiliary information plays a vital role in parameter selection and estimation to achieve efficient estimates of unknown population parameters. Dual use of auxiliary information, i. e., \original" and \ranked" auxiliary variables, helps increase the e, ciency of estimators. In this paper, the performance of di, erence-type-exponential estimators was proposed and evaluated based on dual auxiliary information for population mean Under simple random Sampling. Mathematical expressions for the bias and the mean squared error of the proposed estimators were obtained. Three real-life data sets and Monte Carlo simulation studies were carried out for illustration. The results of empirical and simulation studies indicate that the proposed estimators outperformed their counterparts in terms of mean square errors and percentage relative efficiency.

This article introduces a dual problem of widely used calibration ratio-type estimators for estimating population mean of the study variable considering auxiliary information Under dual constraints using stratified systematic Sampling design. Under large sample approximations, the expression for bias and variance of the proposed estimator are derived. In addition, the optimality condition for the proposed estimator and hence optimum variance expression is also obtained for the same. Moreover, a study based on real-life data is carried out to judge the performance of the proposed calibration estimator in terms of minimum relative bias and relative root mean squared error criterion. The study reveals that the calibration ratio-type estimator Under dual constraints may be preferred in practice as it provides consistent and more precise parameter estimates.

Auxiliary information plays a vital role at the selection and/or estimation stage to achieve the efficient estimates of the unknown population parameters. Dual use of auxiliary information, one the original and second the ranks of the auxiliary variable help to increase the efficiency of the estimators. In this article, we proposed and evaluated the performance of difference-type-exponential estimators based on dual auxiliary information for population mean Under simple random Sampling. Mathematical expressions for the bias and the mean squared error of the proposed estimators are obtained. Three real-life data sets and Monte Carlo simulation studies are carried out for illustration. The results of the empirical and the simulation studies, in terms of mean square errors and percentage relative efficiencies indicate that the proposed estimators perform better as compared to their counterparts.

In this manuscript, a generalized class of estimators has been developed for estimating a finite population means in ranked set Sampling scheme. The expressions for bias and mean square error (MSE) of the proposed class of estimators have been derived up to the first order of approximation. Some estimators are shown to be a member of the proposed class. The proposed class of estimators has been compared through the MSE criterion over the other existing member estimators of the proposed class of estimators. The theoretical conditions are obtained Under which the proposed class of estimators has performed better. Efficiency comparisons, empirical study, and simulation study also delineate the soundness of our proposed generalized class of the estimators Under ranked set Sampling (RSS).

Control charts are widely used to identify changes in the production process, and when it comes to identifying small changes in the process, non-Shewhart control charts such as exponential weighted moving average (EWMA) and generalized weighted moving average (GWMA) are better alternatives to control charts than Shewhart 𝑋 control chart. In this context, nonparametric control charts are used when the distribution of quality characteristic of the process is unknown, in which the Sign control chart is one of the most popular nonparametric control charts. In this paper, for the first time, a generalized weighted moving average sign control chart using a ranked set Sampling (RSS) design is introduced. The performance of the proposed control chart is evaluated using simulated data according to the average run length evaluation criterion, and simulation studies showed that the GWMA sign control chart Under the RSS design is better at detecting small process changes than the EWMA sign control chart Under the RSS design. The performance of the proposed control chart has been evaluated using simulated data according to the average execution length evaluation criteria in Julia software, and the simulation studies show that due to changes in the regulatory parameter α, the 𝐺𝑊𝑀𝐴𝑆𝑅𝑆𝑆 + control chart is more sensitive than the 𝐸𝑊𝑀𝐴𝑆𝑅𝑆𝑆 + control chart in discovering small process changes, also the 𝐺𝑊𝑀𝐴𝑆𝑅𝑆𝑆 + control chart is more sensitive than the 𝐺𝑊𝑀𝐴𝑆𝑆𝑅𝑆 + and 𝐷𝐺𝑊𝑀𝐴𝑆𝑆𝑅𝑆 + control charts are more efficient and sensitive in identifying small process changes, which shows the advantage of RSS scheme over SRS scheme. In addition, it was proved that increasing k and the number of cycles and large values of q decrease 𝐴𝑅𝐿1 and increase the power of the control chart in identifying process changes.

In weighted Sampling as a generalization of random Sampling, every observation, y, is recorded with probably proportional to a non-negative function of y. In this paper, the normal regression model is investigated Under the weighted Sampling for a common weight function. Parameters of the model are estimated for known and unknown weight parameters. Using simulation, efficiency of estimators is studied when they have not closed forms. As an application, the data of number of visited patients by specialist doctors in Social Security Organization of Ahvaz in Iran (SSOAI) are analyzed.

We propose an efficient estimator for population median Under two-phase Sampling when using two auxiliary variables on the lines of Diana [Diana, G. \A class of estimators of the population mean in stratified random Sampling", Statistica, 53(1), pp. 59-66 (1993)] and Jhajj and Walia [Jhajj, H.S. and Walia, G.S. \A generalized difference cum- ratio type estimator for the population variance in double Sampling", Communications in Statistics-Simulations and Computation, 41, pp. 58-64 (2012)]. The expressions for mean squared errors are presented, correct to the first order of approximation. Both theoretical and numerical comparisons reveal that the proposed estimator performs better than the unbiased sample median estimator, ratio estimator, and estimators by Srivastava et al. [Srivastava, S.K., Rani, S., Khare, B.B., and Srivastava, S.R. \A generalized chain ratio estimator for mean of finite population", Journal of the Indian Society of Agricultural Statistics, 42(1), pp. 108-117 (1990)] and Gupta et al. [Gupta, S., Shabbir, J., Ahmad, S. \Estimation of median in two-phase Sampling using two auxiliary variables", Communications in Statistics-Theory and Methods, 37(11), pp. 1815-1822 (2008)].