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Coefficient of variation (CV) control charts are widely used to monitor processes in which the mean of process characteristic varies and its standard deviation changes with the mean. However, such ...

In recent years, the impact of measurement errors on the performance of various control charts have been well evaluated. However, as far as we know, the multiple sampling control charts in the lite...

Skip-lot sampling plans have the provision of inspecting only a fraction of lots, which reduces time and cost of the inspection. Thus, the skip-lot sampling plan is more cost-effective. The intenti...

Adapted from the acceptance sampling field, the double sampling monitoring schemes implement a two-stage strategy to decide whether the process being monitored is in-control or out-of-control. That...

A modified form of the population mean estimator suggested by Anieting and Enang (2020) in stratified double sampling in the presence of nonresponse using a single auxiliary variable has been proposed. The Mean Squared Error (MSE) and the bias of the proposed estimator have been given using large sample approximation. The empirical study shows that the MSE of the suggested estimator is more efficient than all other existing estimators in the same scheme. Determination of the optimal values of the first and second phases samples has also been done

Recent studies have shown that an adaptive T 2 chart with double sampling and variable sampling interval D S V S I T 2 chart shows a good performance in detecting small to moderate shifts in the me...

This study investigates the process for estimating the mean number of individuals having rare sensitive attribute in stratified random sampling as well as in stratified random double sampling using...

In this paper, a ratio-product estimator for estimating the population mean of the study variable based on the population coefficient of skewness of the auxiliary variable is suggested in stratified double sampling. Asymptotic optimum estimator and its approximate bias and variance expressions are derived. Properties of the suggested estimator are studied with some known existing estimators identified as special members of this class of estimators. Analytical and numerical investigations showed that the suggested estimator is more efficient than the conventional regression estimator of mean in stratified double sampling and existing estimators of its class in stratified double sampling. Analysis and evaluation are presented.

This article examines the zero numerator problem. This problem occurs when the misclassification rates are so low that both forms of misclassification may not both be present in the validation data. For this problem, the article compares two Bayesian methods for analyzing misclassified binary data that has a validation sub-study and three forms of a non-informative prior distribution. It shows that the two methods give similar results. However, the posterior distributions were sensitive to the choice of the prior distribution when misclassification rates are low. The article further presents a simulation study that reveals that the bias is small regardless of the considered prior distribution. However, when the misclassification rates are low, the coverage of credible intervals is markedly better for a Jeffreys’ prior than for either a Haldane’s or a uniform prior. Finally, the article highlights the merit of quantifying expert opinion to form a subjective prior distribution when the posterior distribution is sensitive to the prior.

Double sampling for stratification (2SS) is a sampling design that is widely used for forest inventories. We present the mathematical derivation of two appropriate variance estimators for mean growth from repeated 2SS with updated stratification on each measurement occasion. Both estimators account for substratification based on the transition of sampling units among the strata due to the updated allocation. For the first estimator, sizes of the substrata were estimated from the second-phase sample (sample plots), whereas the respective sizes in the second variance estimator relied on the larger first-phase sample. The estimators were empirically compared with a modified version of Cochran’s well-known 2SS variance estimator that ignores substratification. This was done by performing bootstrap resampling on data from two German forest districts. The major findings were as follows: (i) accounting for substratification, as implemented in both new estimators, has substantial impact in terms of significantly smaller variance estimates and bias compared with the estimator without substratification, and (ii) the second estimator with substrata sizes being estimated from the first-phase sample shows a smaller bias than the first estimator.

Count data arising in various fields of applications are often under‐reported. Ignoring undercount naturally leads to biased estimators and inaccurate confidence intervals. In the presence of undercount, in this paper, we develop likelihood‐based methodologies for estimation of mean using validation data. The asymptotic distributions of the competing estimators of the mean are derived. The impact of ignoring undercount on the coverage and length of the confidence intervals is investigated using extensive numerical studies. Finally an analysis of heat mortality data is presented.

In this paper, we design an innovative and general class of modified two-stage sampling schemes to enhance double sampling and modified double sampling procedures. Under the squared error loss plus...

In many applications, the quality of a process is characterized by the functional relationship between a response variable and one or more explanatory variables. This functional relationship is ref...

The present paper deals with the problem of estimating the product of two population means using the information of auxiliary character under double sampling the non-respondents. Two different cases are considered for suggesting the estimators to estimate the product of two population means. The bias and mean square errors are obtained up to the first order of approximation, and the conditions for obtaining the minimum mean square errors of suggested estimators are derived. Theoretical and empirical studies with real data sets published by the Government of India are carried out to demonstrate the efficiency of the proposed estimators over the relevant estimators used in practice.

In sequential tests, typically a (pairwise) multiple comparison procedure (MCP) is performed after an omnibus test (an overall equality test). In general, when an omnibus test (e.g., overall equality of multiple proportions test) is rejected, then we further conduct a (pairwise) multiple comparisons or MCPs to determine which (e.g., proportions) pairs the significant differences came from. In this article, via likelihood-based approaches, we acquire three confidence intervals (CIs) for comparing each pairwise proportion difference in the presence of over-reported binomial data. Our closed-form algorithm is easy to implement. As a result, for multiple-sample proportions differences, we can easily apply MCP adjustment methods (e.g., Bonferroni, &Scaron, id&aacute, k, and Dunn) to address the multiplicity issue, unlike previous literatures. We illustrate our procedures to a real data example.

In statistical process monitoring (SPM), most of the monitoring schemes are designed assuming that the process parameters for the underlying distribution are known (i.e., Case K). In a variety of c...

This paper presents an adaptive T2 control chart for monitoring shifts in the mean vector of a multivariate normally distributed process. This chart which combines the double sampling, variable sam...

Non-linear programming problems can be solved efficiently by geometric programming in which non-linear expressions can be expressed by an exponential or power functions. In this paper, Double Sampling Stratification (DSS) strategy is used in multivariate stratified population with unidentified strata weights, for optimum sampling design (OSD) in the presence of non-response to estimate the unidentified population means. The double sampling problem in the presence of non-response is formulated as Fuzzy Multiobjective Convex Programming Problem (FMOCPP). Then, we convert FMOCPP into Fuzzy Single Objective Convex Problem (FSOCP) by using membership function. Dual solution is obtained using LINGO Software by solving FSOCP. The optimum allocations of sample sizes of respondents and non- respondents for both the phases are obtained by applying dual solutions and primal-dual relationship theorem. The given technique is illustrated by projecting a numerical problem.

The primary aim of this research is to propose a revised triple sampling (TS) X¯ chart, where the derivations of new formulae for computing the average run length of the triple sampling (TS) X¯ chart correctly are provided. The secondary aim is to develop the revised TS X¯ chart with estimated process parameters. The revised TS X¯ charts are compared with the double sampling (DS) X¯, two stage adaptive sample size (AS2) X¯ and three stage adaptive sample size (AS3) X¯ charts when process parameters are known and estimated using the average run length (ARL), average number of observations to signal (ANOS), average of the average run lengths (AARL), standard deviation of the average run lengths (SDARL), average of the average number of observations to signal (AANOS) and standard deviation of the average number of observations to signal (SDANOS) criteria, where the revised TS X¯ charts are found to be superior. Additionally, a table giving the minimum number of Phase-I samples for estimating the process mean so that the revised TS X¯ chart with estimated process parameters has the desired in-control AARL and AANOS performances is provided.

In this study, we suggest a family of ratio estimators for the population mean parameter using various robust regression techniques. These robust regressions techniques are Huber MM, LTS, and LMS estimates. We evaluate the performance of estimators in terms of the mean square error (MSE), and we compare the efficiency of our proposed robust-regression-ratio-type estimators with existing estimators under the optimal conditions. These comparisons show that our robust ratio-type estimators give more efficient results than the existing estimators under double sampling. In addition, the simulation and the empirical studies based on a data set that includes unusual observations show that our proposed estimators have a lower MSE than the existing estimators.

Chain-ratio estimators are often used to improve the efficiency of the estimation of the population total or the mean using two auxiliary variables, available in two different phases. An improved c...

Calibration approach is becoming more important in survey sampling. Calibration estimation helps in improving the estimates of population parameters by making use of auxiliary information. This pap...

This study presents a double sampling (DS) np chart when the process parameter is estimated. The DS np chart is evaluated in terms of the average of the average run length and the standard deviatio...

This paper develops a new double sampling (DS) monitoring scheme, namely, the side-sensitive DS X¯ chart, to monitor the process mean. The operational procedure is presented first followed by the e...

A flexible scrambled response model using a randomization device for quantitative sensitive data is used to evaluate the protection of respondents’ privacy. A double-sampling regression-cum-exponen...

We construct a point and interval estimation using a Bayesian approach for the difference of two population proportion parameters based on two independent samples of binomial data subject to one type of misclassification. Specifically, we derive an easy-to-implement closed-form algorithm for drawing from the posterior distributions. For illustration, we applied our algorithm to a real data example. Finally, we conduct simulation studies to demonstrate the efficiency of our algorithm for Bayesian inference.

This manuscript presents the process for estimating the mean number of individuals having rare sensitive characteristic when population units are heterogeneous with and without prior information on the supplementary (unrelated rare non-sensitive) characteristic. The rare stigmatized parameter is estimated using an ameliorated two-stage randomized response model under stratified sampling and stratified double sampling schemes. The properties of the suggested estimators have been discussed under random, proportional and optimal allocations of sample from different strata. The proposed estimators perform better over some contemporary competent estimators for similar situations which have been shown through empirical studies.

Acceptance sampling plans are quality tools for the manufacturer and the customer. The ultimate result of reduction of nonconforming items will increase the profit of the manufacturer and enhance t...

We have discussed the methods of ACDS and NACS in detail in the previous chapter. In this chapter, we have proposed another new method for estimating the mean/total of the variable of interest. This method is a two-phase variant of the NACS obtained by combining the idea of double sampling and NACS. We have named this method as negative adaptive cluster double sampling (NACDS).

This paper deals with sample size in stratified double sampling in objective function where costs are taken unknown (with and without), respectively. An equivalent deterministic form of objective function has been obtained by using modified E-model in the case of random cost function. Numerical illustrations have been presented.

Shabbir (Commun Stat Theory Methods 47(1):92–101, 2018) suggested a new difference type estimator of finite population mean in stratified double sampling using the ranks of two auxiliary variables as additional information. In this paper, on applying Searls’s (J Am Stat Assoc 59:1225–1226, 1964) approach to Shabbir’s (2018) estimator, we propose an improved estimator of population mean. The expressions of bias and mean square error of the proposed estimator have been obtained, up to first order of approximation. Theoretical and numerical comparisons of the mean square error of the proposed estimator with that of various existing estimators have been made. It is observed that proposed estimator always performs better than Shabbir’s (2018) estimator and also better than most of the other various existing estimators in the literature of survey sampling.

Statistical Process Control (SPC) is widely used in practice, and the control chart is a main tool in SPC. The control chart monitors process quality and detects process variations in real time to reduce the defective products. Regulatory maps are used in clinical trials and agronomic industries, and the mean and variance are not constants, and the coefficient of variation is an indicator of the reliability of chemical tests. However, the coefficient of variation control chart (CV Chart) monitors the coefficient of variation, and the ability to detect small shift sizes is not good. This study uses a double sampling plan combined with a coefficient of variation control chart (DS CV chart) to improve the performance of CV Chart. A design model of DS CV chart is also created to optimize its parameters. The results of the study show that the good performance of DS CV chart in small shift detection.

Statistical Process Control (SPC) is widely used in practice, and the control chart is a main tool in SPC. The control chart monitors process quality and detects process variations in real time to reduce the defective products. Regulatory maps are used in clinical trials and agronomic industries, and the mean and variance are not constants, and the coefficient of variation is an indicator of the reliability of chemical tests. However, the coefficient of variation control chart (CV Chart) monitors the coefficient of variation, and the ability to detect small shift sizes is not good. This study uses a double sampling plan combined with a coefficient of variation control chart (DS CV chart) to improve the performance of CV Chart. A design model of DS CV chart is also created to optimize its parameters. The results of the study show that the good performance of DS CV chart in small shift detection.

An economic-statistical design of the synthetic double sampling (synDS) T2 chart is presented in this study. The cost function is minimized to obtain the optimal design parameters of the synDS T2 c...

The present article deals with the estimation of mean number of respondents who possess a rare sensitive character in presence of known and unknown proportion of a rare unrelated non-sensitive attribute by using the Poisson probability distribution in stratified random sampling as well as in stratified random double sampling. The variance of rare sensitive character is also derived under proportional and optimal allocation methods in stratified random sampling when stratum sizes are known and unknown. The properties of the suggested estimation procedures have been deeply examined. The proposed model is found to be dominant over Lee et al. [Estimation of a rare sensitive attribute in a stratified sample using Poisson distribution. Statistics. 2013;47:575–589] model. Numerical illustrations are presented to support the theoretical results. Results are analysed and suitable recommendations are put forward to the survey practitioners.

A synthetic double sampling (SDS) chart is commonly evaluated based on the assumption that process parameters (namely, mean and standard deviation) are known. However, the process parameters are usually unknown and must be estimated from an in-control Phase-I dataset. This will lead to deterioration in the performance of a control chart. The average run length (ARL) has been implemented as the common performance measure in process monitoring of the SDS chart. Computation of ARL requires practitioners to determine shift size in advance. However, this requirement is too restricted as practitioners may not have the experience to specify the shift size in advance. Thus, the expected average run length (EARL) is introduced to assess the performance of the SDS chart when the shift size is random. In this paper, the SDS chart, with known and estimated process parameters, was evaluated based on EARL and compared with the performance measure, ARL.

The purpose of this paper is to investigate the economic and economic statistical designs of the synthetic double sampling (DS) X‾ chart. The optimal design parameters for the economic design are d...

In this article, we propose a method of planning and determining the optimum parameters of a SkSP-R skip-lot sampling plan by using the attribute double sampling plan as the reference plan. The SkSP-R plan is a new type of skip-lot sampling plan which has a provision for re-inspecting the submitted lots. The optimal plan parameters of the suggested sampling plan are estimated with the target that the average sample number be minimized and satisfying both the specified producer's as well as the consumer's risks simultaneously. In order to obtain the optimum parameters, tables are also built for different combinations of the acceptable quality level and the limiting quality level in conjunctions with different producer's and consumer's risks. An illustrative example is provided for the implementation of the suggested plan. The advantages of the suggested plan over the existing conventional sampling plans and other existing skip-lot sampling plans are also described.

This article deals with the problems of efficient estimation of population variance in two-phase (double) sampling. Using information on two auxiliary variables, a class of chain exponential to regression type estimators has been proposed and its properties are studied under two different structures of two-phase sampling. Superiority of suggested class of estimators over some existing ones is established through numerical illustrations. Suitable recommendations to the survey statistician are also made.