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Three-level control charts have been developed for monitoring processes where the quality of products is characterized by classifying the product characteristic into three discrete levels. In this article, a combined double sampling and variable sampling interval (DSVSI) attribute control chart is developed for monitoring three-level products. This research is motivated by recent studies done on combining the DSVSI scheme with traditional attribute charts and their results recommend the application of the DSVSI attribute charts. The proposed DSVSI three-level chart is compared with the existing standard, adaptive, and EWMA three-level charts. The results approve the superiority of the proposed scheme and recommend it as an efficient three-level control chart in application. An example is also provided to illustrate the application of the proposed chart. [ABSTRACT FROM AUTHOR]

AbstractA process is in its stable state when it has sufficient precision and accuracy. The accuracy is expressed as the deviation of the process mean from its target while the low dispersion indicates the high process precision. Therefore, joint monitoring of multivariate process mean and variability ensures a high rate of producing items. This study proposes a multivariate generalized likelihood ratio scheme called DS-MGLR with two features: (1) considering the effect of imprecise observations, and (2) enhancing the chart sensitivity in reacting to process disturbances. Since the shift magnitude in the distribution parameters is not known in advance, the expected average run length is also calculated for both the MGLR and DS-MGLR charts. To reduce the impact of measurement errors, an improved version of the DS-MGLR chart based on multiple measurement approach is developed. Three comparative studies are presented to indicate the importance of the properties of the developed charts. The first study confirms the efficiency of the double sampling strategy, while the second study indicates the error effect. The third one shows the effectiveness of the multiple measurement approach in compensating for the error contamination. Finally, the applicability of the proposed chart is highlighted using a real data example. [ABSTRACT FROM AUTHOR]

AbstractToday, manufacturers face two challenges: the financial limitation of sampling and the large number of study quality characteristics. In such situations, the problem dimension is usually larger than the sample size, which is known in the literature of statistical quality control as a high dimensional process. The use of conventional multivariate charts to monitor the covariance matrix of such processes is not possible for two reasons: (1) the non-reversibility of the sample covariance matrix, (2) the possibility of the occurrence of sparse shifts in which only a few elements of the covariance matrix are affected. This paper focuses on Phase II monitoring of the covariance matrix of high-dimensional processes based on integrating the ridge penalized likelihood ratio (RPLR) statistic and the combined DS-VSS sampling method, in which DS and VSS features are used concurrently. The performance of the proposed DS-VSS RPLR control chart is compared with the RPLR one in terms of three metrics of the average run length, standard deviation of the run length, and expected value of sample size under three types of joint diagonal/off-diagonal, diagonal and off-diagonal shift patterns. The results show that the DS-VSS scheme is more sensitive than the RPLR in detecting both sparse and non- sparse changes. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Of interest in this paper is the development of a model that uses fixed, then inverse sampling of binary data that is subject to false-positive misclassification in an effort to estimate a proportion. From this model, both the proportion of success and false-positive misclassification rate may be estimated. Also, three first-order likelihood-based confidence intervals for the proportion of success are mathematically derived and studied via a Monte Carlo simulation. The simulation results indicate that the likelihood ratio interval is generally preferable over the Wald and score interval. Lastly, the model is applied to two different real-world medical data sets. [ABSTRACT FROM AUTHOR]

Abstract Double sampling is usually applied to collecting disease information of individuals for situations, in which a gold standard is available for validating a subset of the sample that has been classified by a fallible classifier. Inference procedures are developed for this type of double-sampling data. However, it could happen in practice that such gold standard does not exist. When both false-positive and false-negative diagnoses exist for two classifiers, we propose several likelihood-based and Bayesian methods for estimating the disease prevalence, diagnostic-test sensitivity and specificity under two double-sampling models. A variety of methods including Wald, log-transformation, logit-transformation, inverse-hyperbolic-tangent-transformation, Bootstrap-resampling, Bayesian are proposed to construct confidence intervals (CIs) for these parameters. Moreover, the method of variance estimates recovery (MOVER) is proposed to find the CIs for their difference. The performances of the proposed CIs are evaluated and compared with respect to the empirical coverage probability, coverage width and ratio of mesial non-coverage to non-coverage probability. Empirical results show that all CIs except for Bayesian credible interval with Jeffery non-informative prior and Bootstrap CI based on normality assumption generally produce satisfactory results, and hence be recommended for practical applications. The data from a study of dementia disorders is used to illustrate the proposed methods. [ABSTRACT FROM AUTHOR]

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 is, a master sample is split into two separate subgroup samples, with the first subgroup sample used in the first stage and, depending on which type of double sampling method is used, either only the second or the combined first and second, subgroup sample(s) are used in the second stage. This strategy has been proven to effectively decrease the sampling effort and, at the same time, to decrease the time to detect potential out-of-control situations. For these reasons, it has received some attention in the statistical process monitoring (SPM) literature and, in this review paper, all 92 existing publications on the basic double sampling monitoring schemes and other different schemes that are integrated with the basic double sampling schemes are reviewed. The double sampling schemes are categorized and summarized so that any research gaps in the SPM literature can easily be identified. Finally, concluding remarks and some directions for future research ideas are given. [ABSTRACT FROM AUTHOR]

To estimate the population mean when sampling a heterogeneous population and in the absence of a priori information on auxiliary variables, exponential-ratio multivariate estimators are associated under double stratified sampling with two auxiliary variables. Their biases and mean square errors are expressed and simulated. These mean square errors are smaller (the efficiencies are higher) than those of the sample mean estimator and those of other ratio estimators when the correlation between the study and the auxiliary variables exceeds 0.1 in absolute value. In particular, the proposed estimators are more efficient for low correlations between the study and the auxiliary variables. The gain in efficiency reaches a factor of 230.4% on an empirical dataset where the study variable is weakly correlated with each of the two auxiliary variables, and 182.1% on another empirical dataset where it is strongly correlated. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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 linear cost of sampling, we revisit the classic problem of minimum risk point estimation (MRPE) for an unknown normal mean μ ( ∈ R ) when the population variance σ 2 ( ∈ R + ) also remains unknown. With stopping variables constructed based on an arbitrary general estimator Wm for σ, which satisfies a set of certain conditions, our procedures are proved to enjoy asymptotic first- and second-order efficiency as well as asymptotic first-order risk efficiency. For illustrative purposes, we further investigate specific modified two-stage MRPE procedures, where we substitute appropriate multiples of sample standard deviation, Gini's mean difference (GMD), and mean absolute deviation (MAD) in the place of Wm, respectively. Extensive simulation studies are utilized to validate our theoretical findings. A real-life data set of weight change from female anorexic patients is then analyzed to demonstrate the practical applicability of these modified two-stage MRPE procedures. Comparing them in the case where there exist suspect outliers in the pilot sample, we are empirically confident that the GMD- and MAD-based procedures appear more robust than the sample-standard-deviation-based procedures. [ABSTRACT FROM AUTHOR]

Poisson regression is used to deal with count data. The Poisson regression ratio estimator of the population mean is extended from single to double sampling. This is made possible by the provision of the population mean of an auxiliary variable. The mean square errors of the proposed estimators are expressed up to the first order. Theoretical and numerical results demonstrate that the proposed double-sampling Poisson-regression ratio estimator has a lower mean square error than the double-ratio and the single-sampling estimator. For Covid-19, the minimum mean square errors yielded by the proposed estimator of the total number of cases are 0.095 cases per day and 67.8 cases, compared with 0.112 cases per day and 84.8 cases with the double-ratio estimator. [ABSTRACT FROM AUTHOR]

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 sample size and variable sampling interval features, called the DSVSSI T2 chart and uses three different sample sizes, two different sampling intervals, two warning limits and two different control limits. A Markov chain approach is employed to compute the statistical performance measures. The proposed chart is compared with the existing standard T2 and other adaptive multivariate T2 charts. In all cases, the DSVSSI T2 chart is quicker at detecting small to moderate shifts in the mean vector. An example is provided to illustrate the construction and implementation of the DSVSSI T2 chart. Finally, some concluding remarks are given. [ABSTRACT FROM AUTHOR]

This paper proposes a side-sensitive group runs double sampling (SSGRDS) chart to detect shifts in the process mean. It improves the side-sensitive group runs chart proposed by Gadre and Rattihalli. The implementation of the SSGRDS chart is explained. The newly developed SSGRDS chart is compared with the synthetic, double sampling, synthetic double sampling, side-sensitive group runs and exponentially weighted moving average charts, in terms of the zero-state and steady-state average number of observations to signal (ANOS) and expected average number of observations to signal (EANOS). The zero-state and steady-state ANOS (ssANOS) and EANOS results reveal that the optimal SSGRDS chart generally performs well for detecting small and large mean shifts, from an overall perspective, compared with the optimal versions of other competing charts. This article provides tables of optimal charting parameters to facilitate the design of the SSGRDS chart. From these tables, the user can directly determine the optimal charting parameters for (i) minimising the standardised mean shift , based on different combinations of in-control ANOS and in-control average sample size , or (ii) minimising an overall range of shifts , based on different in-control EANOS and ASS0 combinations. [ABSTRACT FROM AUTHOR]

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 deviation of the average run length. The results show that a large number of Phase-I samples is required for designing the DS np chart. Since it is unrealistic in practice to obtain a large amount of Phase-I data, a combination of new design parameters for the DS np chart with estimated process parameter is computed by taking the number of Phase-I samples into consideration. [ABSTRACT FROM AUTHOR]

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 referred to as a profile. We extend two existing methods for monitoring the shift of slope of linear profiles. We consider the single sampling (SS) and the double sampling (DS) scheme for the economic-statistical design (ESD) model of profile monitoring in Phase II. The results of a numerical example indicate the DS β ^ 1 control chart has better performance than the DS T 2 control chart when ρ β ^ 0 , β ^ 1 is low. Comparison of the ESD of DS β 1 ^ and the SD of DS β 1 ^ control charts show that an ESD has an improvement over the pure SD. Also, we compare the ESD of the DS β 1 ^ with the ESD of the SS β 1 ^ control chart. The results show that the DS β 1 ^ control charts are more efficient in terms of minimizing the E (L). [ABSTRACT FROM AUTHOR]

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 paper proposes a new calibration estimator for estimating the population mean in the stratified random sampling with a set of new calibration constraints using known coefficient of variation of the auxiliary variable. The result has also been extended to the case of double sampling in stratified sampling. The proposed estimator has been compared with the estimator developed by Tracy et al. (2003) with the help of simulation study on real datasets. [ABSTRACT FROM AUTHOR]

Control charts based on inspection with gauges are an interesting alternative to monitor quantitative variables when measurement is complex or expensive. The main advantage over variable control charts lies in greater operational simplicity and economy. However, gauge-based control charts are usually less powerful in order to detect shifts in the process than variables control charts, when the same sample size is used. To improve its performance, the use of double sampling on gauge-based monitoring is proposed. The new chart shows better performance than X ¯ , S and X ¯ − S charts, for the same average sample size, keeping low sampling cost. [ABSTRACT FROM AUTHOR]

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 chart by incorporating the statistical constraints or the constraints on the average number of samples. An example is provided and a sensitivity analysis is conducted to study the effect of model parameters on the optimal solution of the design. The numerical comparison shows that the synDS T2 chart performs better than the synthetic T2 chart and the multivariate exponentially weighted moving average chart, in terms of the cost. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

A side-sensitive modified group runs double sampling (SSMGRDS) chart for detecting mean shifts is proposed. The average number of observations to signal (ANOS) and expected average number of observations to signal (EANOS) performances of the SSMGRDS, , double sampling (DS), side-sensitive group runs double sampling (SSGRDS), side-sensitive modified group runs (SSMGR) and exponentially weighted moving average (EWMA) charts are compared. For the zero-state case, the SSMGRDS chart outperforms all charts under comparison, for all sizes of mean shifts. For the steady-state case, the EWMA chart prevails for small and moderate mean shifts but the SSMGRDS chart prevails for large shifts. [ABSTRACT FROM AUTHOR]

This study presents a control chart for monitoring shifts in the covariance matrix of a multivariate normally distributed process. This chart combines the double sampling, variable sample size and variable sampling interval features, and is called the DSVSSI |S| chart. A Markov chain approach is developed to design the DSVSSI |S| chart, by minimizing the average time to signal (ATS), for a specified shift size in the covariance matrix. The DSVSSI |S| chart has a better ATS performance compared to other existing charts. An example is given to illustrate the operation of the DSVSSI |S| chart. [ABSTRACT FROM AUTHOR]

This study proposes a double sampling (DS) Max chart for monitoring shifts in the process mean and standard deviation. The design of the DS Max chart depends on five parameters, i.e. first and second sample sizes, warning limit at Stage 1, upper control limits at Stages 1 and 2. The optimization design of the DS Max chart is conducted using a genetic algorithm by minimizing the average run length. The comparison shows that the DS Max chart performs better than the existing charts in the literature. An example is provided to illustrate the application of the DS Max chart. [ABSTRACT FROM AUTHOR]

A combined double sampling and variable sampling interval (DSVSI) np chart is investigated in this study. The optimal design of the DSVSI np chart is based on minimizing the out-of-control average time to signal. From the numerical results, the DSVSI np chart performs reasonably well in comparison with the standard np chart, double sampling np chart, synthetic double sampling np chart, and other existing np type control charts for detecting increases in the process of fraction non conforming, based on the zero-state case. An example is provided to illustrate the application of the DSVSI np chart. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of estimating the population varianceS2yof the study variableyusing auxiliary information in sample surveys. We have suggested a class of estimators of the population varianceS2yof the study variableywhen the population varianceS2xof the auxiliary variablexis known. Asymptotic expressions of bias and mean squared error (MSE) of the proposed class of estimators have been obtained. Asymptotic optimum estimators in the proposed class of estimators have also been identified along with its MSE formula. A comparison has been provided. We have further provided the double sampling version of the proposed class of estimators. The properties of the double sampling version have been provided under large sample approximation. In addition, we support the present study with aid of a numerical illustration. [ABSTRACT FROM AUTHOR]

Although the classical Shewhart np control chart has been widely used to detect an out-of-control status of manufacturing process, it is static and there is lack of responsiveness to slight process changes. In this paper, an adaptive np control chart with a joint sampling strategy combining double sampling (DS) and variable sampling interval (VSI) is developed. The multiple dependent state sampling scheme is adopted to further improve the performance of the control chart. An economical design model to minimize the general cost of using the proposed chart is established and solved by a genetic algorithm. The numerical results show that comparing to traditional static np control chart, the proposed np chart yields better performance in terms of shorter time to signal an out-of-control process and less expected cost per unit of time. Comparisons are made to show the capability of the proposed chart in yielding average reductions of 5.01% and 8.89%, in the cost of the proposed model compared to situations in which either the DSVSI np chart or the traditional np chart is used. [ABSTRACT FROM AUTHOR]

Semi-competing risks data arise when two types of events, non-terminal and terminal, may be observed. When the terminal event occurs first, it censors the non-terminal event. Otherwise the terminal event is observable after the occurrence of the non-terminal event. In practice, it can be hard to ascertain all terminal event information after the non-terminal event. Yu and Yiannoutsos [(2015), ‘Marginal and Conditional Distribution Estimation from Double-Sampled Semi-Competing Risks Data’,Scandinavian Journal of Statistics, 42, 87–103] considered a setting when the terminal event is ascertained via double sampling from only a subset of patients who experienced the non-terminal event. They discussed estimation for marginal and conditional distributions under this double sampled semi-competing risk data framework. We propose a more efficient estimation method in the same setting by fully utilising the non-terminal event information. The efficiency gain can be substantial as observed in our simulation study. [ABSTRACT FROM AUTHOR]

A two-stage randomized response model is extended to stratified random sampling in order to find out more efficient estimators of proportions built from sensitive questions, which respondents may not answer truthfully, in a population divided into homogeneous subgroups. In each subgroup, the respondents who have not answered the sensitive question in the first stage are requested in the second stage to either answer the sensitive question (second attempt then) or to draw a card indicating “yes” or “no”. In the latter case, they are required to report the outcome. Such extension provides a more efficient estimator of the proportion of the population having a given sensitive attribute than its counterpart in simple random sampling. The extended two-stage randomized response model is more efficient than the stratified randomized response model, where respondents must answer the sensitive question either in the first or in the second stage. Moreover, it increases the respondents’ cooperation. When strata weights are unknown, they are estimated by the double sampling method. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a version of Hayter and Tsui's statistical test with double sampling for the vector mean of a population under multivariate normal assumption. A study showed that this new test was more or as efficient than the well-known Hotelling'sT2with double sampling. Some nice features of Hayter and Tsui's test are its simplicity of implementation and its capability of identifying the errant variables when the null hypothesis is rejected. Taking that into consideration, a new control chart called HTDS is also introduced as a tool to monitor multivariate process vector mean when using double sampling. [ABSTRACT FROM AUTHOR]

The present investigation deals with the problem of estimation of population mean in two-phase sampling. In the presence of two auxiliary variables, some classes of estimators have been proposed through predictive approach. Properties of the proposed classes of estimators have been studied, and the unbiased versions of these estimators along with their approximate variance expressions are obtained under simple random sampling without replacement scheme. The respective optimum strategies of the proposed estimators are discussed, and their empirical and graphical comparisons with some contemporary estimators of population mean have been made. Suitable recommendations to the survey practitioner are given. [ABSTRACT FROM PUBLISHER]

We suggested the class of estimators of the population mean with its bias and mean square error. It has been shown that the suggested class is more efficient than the usual unbiased, ratio, product and regression estimators and estimators due to Bahl and Tuteja (1991), Singh et al. (2009), and Upadhyaya et al. (2011). In addition an empirical study also carried out to and founded that the members of suggested family also have improvement over Grover and Kaur (2011) and Shabbir and Gupta (2011) classes. Two-phase (double) sampling version of the proposed class was also given. [ABSTRACT FROM PUBLISHER]

In this article, a chain ratio-product type exponential estimator is proposed for estimating finite population mean in stratified random sampling with two auxiliary variables under double sampling design. Theoretical and empirical results show that the proposed estimator is more efficient than the existing estimators, i.e., usual stratified random sample mean estimator, Chand (1975) chain ratio estimator, Choudhary and Singh (2012) estimator, chain ratio-product-type estimator, Sahoo et al. (1993) difference type estimator, and Kiregyera (1984) regression-type estimator. Two data sets are used to illustrate the performances of different estimators. [ABSTRACT FROM AUTHOR]

In stratified sampling when strata weights are unknown a double sampling technique may be used to estimate them. A large simple random sample from the unstratified population is drawn and units falling in each stratum are recorded. A stratified random sample is then selected and simple random subsamples are obtained out of the previously selected units of the strata. This procedure is called double sampling for stratification. If the problem of non-response is there, then subsamples are divided into classes of respondents and non-respondents. A second subsample is then obtained out of the non-respondents and an attempt is made to obtain the information by increasing efforts, persuasion and call backs. In this paper, the problem of obtaining a compromise allocation in multivariate stratified random sampling is discussed when strata weights are unknown and non-response is present. The problem turns out to be a multiobjective non-linear integer programming problem. An approximation of the problem to an integer linear programming problem by linearizing the non-linear objective functions at their individual optima is worked out. Chebyshev's goal programming technique is then used to solve the approximated problem. A numerical example is also presented to exhibit the practical application of the developed procedure. [ABSTRACT FROM AUTHOR]

In this article, an adaptivechart which combines variable sample sizes, sampling intervals, and double sampling features called CVSSIDS control chart is proposed, which uses three different sample sizes, two different sampling intervals, two warning limits, and two different control limits. To evaluate the efficiency of the proposed scheme versus different schemes, average time to signal, average number of samples to signal and average number of observations to signal are utilized. In addition, the minimum ATS values of the proposed chart are computed. Finally, the proposed chart is compared to standard Shewhart (SS) chart and several adaptive control charts. [ABSTRACT FROM AUTHOR]

A combination of double sampling and variable sampling interval (DSVSI) charts can increase the efficiency of signaling small shifts. This study proposes an economic-statistical model for designing joint DSVSI ... and s charts. The proposed approach uses the economic model developed by Duncan in 1956. Research results indicate that the economic-statistical design of the joint DSVSI ... and s charts outperformed traditional economic design approach in detection abilities of process shifts; variable cost (a2), expected costs resulting from defective products when the process was in control (C0), and the expected number of assignable causes (λ) have the major influence on cost E(C′); deviations (δ, γ) significantly influenced cost E(C′); and statistical limitations (AATS*IC; AATS*OOC) do not substantially affect cost E(C′). [ABSTRACT FROM AUTHOR]

Detectability issues create uncertainty in field surveys of animal and plant populations. Detectability correction is one method employed to deal with this problem when there is reasonable certainty that detectability is roughly constant with time or in different areas. Two new reduced-variance estimators of detectability are introduced and evaluated for the case of using a detectability correction for new areas that are surveyed only once. The new estimates are unbiased or nearly unbiased and produce population estimates with smaller variance than the Lincoln–Petersen estimate. [ABSTRACT FROM AUTHOR]

We consider data with a nominal grouping variable and a binary response variable. The grouping variable is measured without error, but the response variable is measured using a fallible device subject to misclassification. To achieve model identifiability, we use the double-sampling scheme which requires obtaining a subsample of the original data or another independent sample. This sample is then classified by both the fallible device and another infallible device regarding the response variable. We propose two Wald tests for testing the association between the two variables and illustrate the test using traffic data. The Type-I error rate and power of the tests are examined using simulations and a modified Wald test is recommended. [ABSTRACT FROM AUTHOR]

Investigating the prevalence of a disease is an important topic in medical studies. Such investigations are usually based on the classification results of a group of subjects according to whether they have the disease. To classify subjects, screening tests that are inexpensive and nonintrusive to the test subjects are frequently used to produce results in a timely manner. However, such screening tests may suffer from high levels of misclassification. Although it is often possible to design a gold-standard test or device that is not subject to misclassification, such devices are usually costly and time-consuming, and in some cases intrusive to the test subjects. As a compromise between these two approaches, it is possible to use data that are obtained by the method of double-sampling. In this article, we derive and investigate four test statistics for testing a hypothesis on disease prevalence with double-sampling data. The test statistics are implemented through both the asymptotic method suitable for large samples and approximate unconditional method suitable for small samples. Our simulation results show that the approximate unconditional method usually produces a more satisfactory empirical type I error rate and power than its asymptotic counterpart, especially for small to moderate sample sizes. The results also suggest that the score test and the Wald test based on an estimate of variance with parameters estimated under the null hypothesis outperform the others. An real example is used to illustrate the proposed methods. [ABSTRACT FROM AUTHOR]

We consider two-sample binary data consisting of two independent studies. One study is the main study where individuals are classified using a fallible classifier prone to error; the other study is a validation study where individuals are classified using both the fallible classifier and a gold standard which does not misclassify individuals. For such data, we propose a Bayesian model for making statistical inference for all model parameters and particularly the risk difference. We derive a closed-form algorithm for sampling from the posterior distribution. We then illustrate our algorithm using a real data example and conduct Monte Carlo simulation studies to show that our algorithm performs very well under various scenarios. [ABSTRACT FROM PUBLISHER]

Using double sampling technique, a generalized difference-cum-ratio type estimator has been proposed for estimating the population mean. The expressions for bias and mean square error of proposed estimator have been obtained. The conditions under which proposed estimator is better than the regression estimator and mean per unit estimator have also been obtained. The gain in efficiency over the existing ones have been illustrated numerically as well as graphically. Simulation study has also been done to support the results by generating data. [ABSTRACT FROM AUTHOR]

We consider Bayesian point and interval estimation for a risk ratio of two proportion parameters using two independent samples of binary data subject to misclassification. In order to obtain model identifiability, we apply a double sampling scheme. For the identifiable model, we propose a Bayesian method for statistical inference for a two proportion risk ratio. Specifically, we derive an easy-to-implement closed-form sampling algorithm to draw from the posterior distribution of interest. We demonstrate the efficiency of our algorithm for Bayesian inference via Monte Carlo simulation studies and using a real data example. [ABSTRACT FROM AUTHOR]

In this article, we propose a double-sampling (DS) np control chart. We assume that the time interval between samples is fixed. The choice of the design parameters of the proposed chart and also comparisons between charts are based on statistical properties, such as the average number of samples until a signal. The optimal design parameters of the proposed control chart are obtained. During the optimization procedure, constraints are imposed on the in-control average sample size and on the in-control average run length. In this way, required statistical properties can be assured. Varying some input parameters, the proposed DS np chart is compared with the single-sampling np chart, variable sample size np chart, CUSUM np and EWMA np charts. The comparisons are carried out considering the optimal design for each chart. For the ranges of parameters considered, the DS scheme is the fastest one for the detection of increases of 100% or more in the fraction non-conforming and, moreover, the DS np chart is easy to operate. [ABSTRACT FROM AUTHOR]

Shabbir and Gupta (2007) introduced an exponential ratio-type estimator for the population variance and compare its mean square error with mean square error of some of the existing estimators. But unfortunately, the expression of mean square error of their proposed estimator is incorrect and hence the comparison based on incorrect mean square error, carried by them, is wrong. In the present article, the author provides the correct expression of the mean square error, up to first order of approximation, of the same estimator. A comparison has been made by taking the corrected expression of mean square error. The corresponding exponential ratio-type estimator for the population variance, under double sampling technique, is also proposed which followed by a comparison. [ABSTRACT FROM AUTHOR]

With the relatively recent widespread availability of operational fine spatial resolution imagery from satellites, there is more opportunity to conduct spatial sampling with combinations of spatial resolution data. This method is generally called regression estimation. Regression estimation consists of first using a coarser spatial resolution sensor over a large area. For selected samples, a second delineation is done with a finer spatial resolution system which is presumed to be more accurate. A statistical comparison of the two estimates for the selected sample areas is made and if a suitable relationship exists, a correction factor can be determined and applied to the full study area. This manuscript reviews the regression estimation process and provides a case study. The case study used the technique to determine the extent of the winter rice crop in Bangladesh with Landsat data and statistics provided for local administrative units by agricultural agents. [ABSTRACT FROM AUTHOR]

Consider independent observations X1, X2,... having a common normal probability density function [image omitted] with - ∞ < x < ∞ and unknown variance σ2 ( > 0). We propose to estimate f(x;σ2) by a plug-in maximum likelihood (ML) two-stage estimator under the mean integrated squared error (MISE) loss function. Our goal is to make the associated risk not to exceed a preassigned positive number c, referred to as the risk-bound. Because no fixed-sample-size methodology would handle this estimation problem, we design an appropriate two-stage estimation methodology that is shown to satisfy the asymptotic (i) first-order efficiency property (Theorem 2.1), (ii) first-order risk-efficiency property (Theorem 2.2), as well as (iii) second-order efficiency property (Theorem 2.3). The performances of the proposed methodology for small, moderate, and large sample sizes are examined with the help of simulations. We have noticed some limited robustness of the proposed methodology under mixture-normal population densities, in which case the asymptotic second-order efficiency property (Theorem 3.1) is shown. Illustrations are included with real data and analysis. Overall, we feel that the proposed two-stage plug-in density estimation methodology performs remarkably well. [ABSTRACT FROM AUTHOR]

The present study deals with the use of high-resolution satellite imagery in forest inventory of the open savanna woodlands of southern Africa. The study was carried out in Hans Kanyinga Community Forest, north-eastern Namibia. A two-phase (double) sampling design was used to estimate the variables of interest, namely stand volume, stand density and diameter distribution. QuickBird satellite images were used to extract auxiliary variables (image data), such as photogrammetric crown diameter and number of stems, using visual interpretation and measuring tools offered by Erdas 8.7 geographic imaging software. Field inventory data (terrestric data) collected in 2002 were used to obtain the terrestric data. Stepwise regression and correlation analysis between satellite imagery and field data was carried out and the results were moderate. The stand volume model explained 56%, the stand density model 81% and the diameter distribution model 43% of the variation. Cost-efficiency assessment of double sampling with regression estimators showed a considerable reduction in inventory costs by up to 24% compared to a traditional forest inventory method in Hans Kanyinga Community Forest. Double sampling was found to be cost-efficient when the proportion of variability of the models was higher than 27%. The inventory concept showed potential in providing information required both at the higher and lower levels of forest management. Follow up research is required. [ABSTRACT FROM AUTHOR]

In this article, we consider the T2 chart with double sampling to control bivariate processes (BDS chart). During the first stage of the sampling, n1 items of the sample are inspected and two quality characteristics (x; y) are measured. If the Hotelling statistic [image omitted] for the mean vector of (x; y) is less than w, the sampling is interrupted. If the Hotelling statistic [image omitted] is greater than CL1, where CL1>w, the control chart signals an out-of-control condition. If [image omitted] , the sampling goes on to the second stage, where the remaining n2 items of the sample are inspected and [image omitted] for the mean vector of the whole sample is computed. During the second stage of the sampling, the control chart signals an out-of-control condition when the statistic [image omitted] is larger than CL2. A comparative study shows that the BDS chart detects process disturbances faster than the standard bivariate T2 chart and the adaptive bivariate T2 charts with variable sample size and/or variable sampling interval. [ABSTRACT FROM AUTHOR]

In this article, we introduce minimum divergence estimators of parameters of a binary response model when data are subject to false-positive misclassification and obtained using a double-sampling plan. Under this set up, the problem of goodness-of-fit is considered and divergence-based confidence intervals (CIs) for a population proportion parameter are derived. A simulation experiment is carried out to compare the coverage probabilities of the new CIs. An application to real data is also given. [ABSTRACT FROM AUTHOR]

We provide a method for finding the optimal double sampling plan for estimating the mean value of a continuous outcome. It is assumed that the fallible and true outcome data are related by a multivariate linear regression model where only some of the explanatory variables are sampled. Conditions under which double sampling is preferred over standard sampling plans are determined. An application of the method to a well-known data set on air pollution is presented. [ABSTRACT FROM AUTHOR]

two-phase sampling, the second-phase sample is often a stratified sample based on the information observed in the first-phase sample. For the total of a population characteristic, either the double-expansion estimator or the reweighted expansion estimator can be used. Given a consistent first-phase replication variance estimator, we propose a consistent variance estimator that is applicable to both the double-expansion estimator and the reweighted expansion estimator. The proposed method can be extended to multiphase sampling. [ABSTRACT FROM AUTHOR]