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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...

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...

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.

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...

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...

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...

To estimate the disease prevalence, a gold standard test is the best choice for accurate estimation. The gold standard could be very expensive or time consuming for use in practice. For this reason...

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...

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...

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.

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.

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.

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 seco...

This paper addresses the problem of estimating the population variance S2y of the study variable y using auxiliary information in sample surveys. We have suggested a class of estimators of the population variance S2y of the study variable y when the population variance S2x of the auxiliary variable x is 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.

This paper suggests a stratified Kuk model to estimate the proportion of sensitive attributes of a population composed by a number of strata; this is undertaken by applying stratified sampling to the adjusted Kuk model. The paper estimates sensitive parameters when the size of the stratum is known by taking proportional and optimal allocation methods into account and then extends to the case of an unknown stratum size, estimating sensitive parameters by applying stratified double sampling and checking the two allocation methods. Finally, the paper compares the efficiency of the proposed model to that of the Su, Sedory and Singh model and the adjusted Kuk model in terms of the estimator variance. Este trabajo propone un modelo Kuk estratificado para estimar la proporción de atributos sensibles de una población compuesta por varios estratos mediante la aplicación de un muestreo estratificado al modelo Kuk ajustado. El trabajo estima parámetros sensibles en el caso en que el tamaño del estrato es conocido mediante la adopción de métodos de asignación proporcionales y óptimos, y se extiende al caso de un tamaño de estrato desconocido, estimando parámetros sensibles mediante la aplicación de un doble muestreo estratificado y la comprobación de los dos métodos de asignación. Por último, el trabajo compara la eficiencia del modelo propuesto a la del modelo de Su, Sedory y Singh y el modelo Kuk ajustado en términos de la varianza del estimador.

Ratio-product-ratio estimators with two parameters in double sampling under non-response are considered along with their properties. Practical conditions are obtained in which the suggested estimators are more proficient than other existing estimators. An example is given.

Non-ignorable dropout is common in studies with long follow-up time, and it can bias study results unless handled carefully in the study design and the statistical analysis. A double-sampling design allocates additional resources to pursue a subsample of the dropouts and find out their outcomes, which can address potential biases due to non-ignorable dropout. It is desirable to construct semiparametric estimators for the double-sampling design because of their robustness properties. However, obtaining such semiparametric estimators remains a challenge due to the requirement of the analytic form of the efficient influence function (EIF), the derivation of which can be ad hoc and difficult for the double-sampling design. Recent work has shown how the derivation of EIF can be made deductive and computerizable using the functional derivative representation of the EIF in nonparametric models. This approach, however, requires deriving the mixture of a continuous distribution and a point mass, which can itself be challenging for complicated problems such as the double-sampling design. We propose semiparametric estimators for the survival probability in double-sampling designs by generalizing the deductive and computerizable estimation approach. In particular, we propose to build the semiparametric estimators based on a discretized support structure, which approximates the possibly continuous observed data distribution and circumvents the derivation of the mixture distribution. Our approach is deductive in the sense that it is expected to produce semiparametric locally efficient estimators within finite steps without knowledge of the EIF. We apply the proposed estimators to estimating the mortality rate in a double-sampling design component of the President’s Emergency Plan for AIDS Relief (PEPFAR) program. We evaluate the impact of double-sampling selection criteria on the mortality rate estimates. Simulation studies are conducted to evaluate the robustness of the proposed estimators.

A disease prevalence can be estimated by classifying subjects according to whether they have the disease. When gold-standard tests are too expensive to be applied to all subjects, partially validated data can be obtained by double-sampling in which all individuals are classified by a fallible classifier, and some of individuals are validated by the gold-standard classifier. However, it could happen in practice that such infallible classifier does not available. In this article, we consider two models in which both classifiers are fallible and propose four asymptotic test procedures for comparing disease prevalence in two groups. Corresponding sample size formulae and validated ratio given the total sample sizes are also derived and evaluated. Simulation results show that (i) Score test performs well and the corresponding sample size formula is also accurate in terms of the empirical power and size in two models; (ii) the Wald test based on the variance estimator with parameters estimated under the null hypothesis outperforms the others even under small sample sizes in Model II, and the sample size estimated by this test is also accurate; (iii) the estimated validated ratios based on all tests are accurate. The malarial data are used to illustrate the proposed methodologies.

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 simulatio...

This study proposes a synthetic double sampling s chart that integrates the double sampling (DS) s chart and the conforming run length chart. An optimization procedure is proposed to compute the optimal parameters of the synthetic DS s chart. The performance of the synthetic DS s chart is compared with other existing control charts for monitoring process standard deviation. The results show that the synthetic DS s chart is more effective for detecting increases in the process standard deviation for a wide range of shifts. An example is provided to illustrate the operation procedure of the synthetic DS s chart.

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.

This paper proposes useful exact bounds for the parameters of the double sampling S2 chart with known process variance and it also investigates the properties of the double sampling S2 chart with e...

Wald, profile likelihood, and marginal likelihood confidence intervals are derived for the ratio of two Poisson rates in the presence of one-way differentially misclassified data using double sampling. Monte Carlo simulations demonstrate the reliability and relative performance of the intervals, and an example from cancer epidemiology illustrates their application and interpretation in a real-world scenario. All of the methods described are implemented and freely available in the R package poisDoubleSamp on the Comprehensive R Archive Network (CRAN).

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.

The implementation of an adaptive cluster sampling design often becomes logistically challenging because variation in the final sampling effort introduces uncertainty in survey planning. To overcome this drawback, an inexpensive and easy to measure auxiliary variable could be used in a two-phase survey strategy, called adaptive cluster double sampling (Felix-Medina and Thompson in Biometrika 91:877–891, 2004). In this paper, a two-phase sampling strategy is proposed which combines the idea of adaptive cluster double sampling with the principle of post-stratification. In the first-phase an adaptive cluster sample is selected by means of an inexpensive auxiliary variable. Networks from the first phase sampling are then post-stratified according to their size. In the second-phase, the network structure is used to select a subsample of units by means of stratified random sampling. The proposed sampling strategy employs stratification without requiring an a priori delineation of the strata. Indeed, the strata sizes are estimated in the course of the two-phase sampling process. Therefore, it is suitable for situations where stratification is suspected to be efficient but strata cannot be easily delineated in advance. In this framework, a new type of estimator for the population mean which mimics the stratified sampling mean estimator and an estimator of the sampling variance are proposed. The results of a simulation study confirm, as expected, that the use of post-stratification leads to gain in precision for the estimator. The proposed sampling strategy is applied for targeting an epiphytic lichen community Lobarion pulmonariae in a forest area of the Northern Apennines (N-Italy), characterized by several species of conservation concern.

In this article, a new attributes double sampling plan for three-class products (ADSPTP) is presented, and the corresponding operating characteristic function is constructed based on the given procedure of performing ADSPTP. Average sample numbers (ASN) for complete inspection and curtailed inspection of the second sample are derived and the extreme point is discussed on the three-dimensional ASN surface. In addition, the differences arising from different parameters are studied. Sampling plans are designed by a nonlinear optimization model. Finally, numerical examples and discussions are given to illustrate the obtained results, and tables of the designed plans under various conditions are provided.

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's T2 with 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.

In this paper, we consider the problem of estimation of population mean of a study variable by making use of first-phase sample mean and first-phase sample median of the auxiliary variable at the estimation stage. The proposed new estimator of the population mean is compared to the sample mean estimator, ratio estimator and the difference type estimator for the fixed cost of the survey by using the concept of two-phase sampling. The magnitude of the relative efficiency of the proposed new estimator has been investigated through simulation study.

Bayesian acceptance sampling plans, which utilize prior information on the process variation, can be employed as an alternative to conventional types of plans for taking decisions on the disposition of submitted lots. A special type of double sampling inspection plans by attributes with small acceptance numbers using Bayesian methodology is presented in this paper emphasizing its significance over small acceptance number single sampling plans. The procedures for designing such sampling plans for specified degree of discrimination which would ensure protection to the producer and consumer are discussed with illustrations under the conditions for the application of gamma-Poisson distribution.

This paper discusses the problem of estimation of finite population mean in double sampling for stratification. In fact, ratio and product type exponential estimators of population mean are proposed in double sampling for stratification. The biases and mean squared errors of proposed estimators are obtained upto the first degree of approximation. The proposed estimators have been compared with usual unbiased estimator, ratio and product estimators in double sampling for stratification. To judge the performance of the proposed estimators an empirical study has been carried out.