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Maintaining high levels of process quality is crucial to the competitiveness of manufacturing firms in today's increasingly global marketplace. To ensure the quality of manufactured products meets customer needs, process capability indices (PCIs) are widely used to analyze the process performance of various processing characteristics. Products characterise by processing characteristics of both unilateral and bilateral specifications are common in the current sales market. Manufacturing firms must often adopt multiple PCIs to analyze the process performance of a single product, which is inefficient in practical applications and management. Yield-based index C p k is not subject to this limitation. For this reason, we employed C p k to evaluate process performance and the effectiveness of improvement measures. In practice, C p k is estimated from samples, which means that misjudgment may occur in the assessment of process performance and improvement effectiveness due to sampling errors. We therefore derived the 100 (1 − α) % confidence interval of C p k and, based on the producer's perspective, used the upper confidence limit to evaluate improvement effectiveness. To lower the risk of misjudgment and increase the reliability of improvement effectiveness in the case of data uncertainty, this paper further proposes fuzzy estimation using the right-sided confidence interval of C p k and develops the fuzzy judgement model. [ABSTRACT FROM AUTHOR]

The rapid progression of emerging technologies like the Internet of Things (IoT) and Big Data analytics for manufacturing has driven innovation across various industries worldwide. Production data are utilized to construct a model for quality evaluation and analysis applicable to components processed by machine tools, ensuring process quality for critical components and final product quality for the machine tools. Machine tool parts often encompass several quality characteristics concurrently, categorized into three types: smaller-the-better, larger-the-better, and nominal-the-better. In this paper, an evaluation index for the nominal-the-better quality characteristic was segmented into two single-sided Six Sigma quality indexes. Furthermore, the process quality of the entire component product was assessed by n single-sided Six Sigma quality indexes. According to numerous studies, machine tool manufacturers conventionally base their decisions on small sample sizes (n), considering timeliness and costs. However, this often leads to inconsistent evaluation results due to significant sampling errors. Therefore, this paper established fuzzy testing rules using the confidence intervals of the q single-sided Six Sigma quality indices, serving as the fuzzy quality evaluation model for components of machine tools. [ABSTRACT FROM AUTHOR]

With clustered data, such as where students are nested within schools or employees are nested within organizations, it is often of interest to estimate and compare associations among variables separately for each level. While researchers routinely estimate between-cluster effects using the sample cluster means of a predictor, previous research has shown that such practice leads to biased estimates of coefficients at the between level, and recent research has recommended the use of latent cluster means with the multilevel structural equation modeling framework. However, the latent cluster mean approach may not always be the best choice as it (a) relies on the assumption that the population cluster sizes are close to infinite, (b) requires a relatively large number of clusters, and (c) is currently only implemented in specialized software such as Mplus. In this paper, we show how using empirical Bayes estimates of the cluster means can also lead to consistent estimates of between-level coefficients, and illustrate how the empirical Bayes estimate can incorporate finite population corrections when information on population cluster sizes is available. Through a series of Monte Carlo simulation studies, we show that the empirical Bayes cluster-mean approach performs similarly to the latent cluster mean approach for estimating the between-cluster coefficients in most conditions when the infinite-population assumption holds, and applying the finite population correction provides reasonable point and interval estimates when the population is finite. The performance of EBM can be further improved with restricted maximum likelihood estimation and likelihood-based confidence intervals. We also provide an R function that implements the empirical Bayes cluster-mean approach, and illustrate it using data from the classic High School and Beyond Study. [ABSTRACT FROM AUTHOR]

Epidemiologic screening programs often make use of tests with small, but nonzero probabilities of misdiagnosis. In this article, we assume the target population is finite with a fixed number of true cases, and that we apply an imperfect test with known sensitivity and specificity to a sample of individuals from the population. In this setting, we propose an enhanced inferential approach for use in conjunction with sampling-based bias-corrected prevalence estimation. While ignoring the finite nature of the population can yield markedly conservative estimates, direct application of a standard finite population correction (FPC) conversely leads to underestimation of variance. We uncover a way to leverage the typical FPC indirectly toward valid statistical inference. In particular, we derive a readily estimable extra variance component induced by misclassification in this specific but arguably common diagnostic testing scenario. Our approach yields a standard error estimate that properly captures the sampling variability of the usual bias-corrected maximum likelihood estimator of disease prevalence. Finally, we develop an adapted Bayesian credible interval for the true prevalence that offers improved frequentist properties (i.e., coverage and width) relative to a Wald-type confidence interval. We report the simulation results to demonstrate the enhanced performance of the proposed inferential methods. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Health & Nursing Management / Sağlık ve Hemşirelik Yönetimi Dergisi is the property of Logos Medical Publishing and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The process capability index is a tool for quality measurement and analysis widely used in the industry. It is also a good tool for the sales department to communicate with customers. Although the value of the process capability index can be affected by the accuracy and precision of the process, the index itself cannot be differentiated. Therefore, the process incapability index is directly divided into two items, accuracy and precision, based on the expected value of the Taguchi process loss function. In fact, accuracy and precision are two important reference items for improving the manufacturing process. Thus, the process incapability index is good for evaluating process quality. The process incapability index contains two unknown parameters, so it needs to be estimated with sample data. Since point estimates are subject to misjudgment incurred by the inaccuracy of sampling, and since modern businesses are in the era of rapid response, the size of sampling usually tends to be small. A number of studies have suggested that a fuzzy testing method built on the confidence interval be adopted at this time because it integrates experts and the experience accumulated in the past. In addition to a decrease in the possibility of misjudgment resulting from sampling error, this method can improve the test accuracy. Therefore, based on the confidence interval of the process incapability index, we proposed the fuzzy testing method to assess whether the process capability can attain a necessary level of quality. If the quality level fails to meet the requirement, then an improvement must be made. If the quality level exceeds the requirement, then it is equivalent to excess quality, and a resource transfer must be considered to reduce costs. [ABSTRACT FROM AUTHOR]

Policy makers, firms, and researchers often choose among multiple options based on estimates. Sampling error in the estimates used to guide choice leads to a winner's curse, since we are more likely to select a given option precisely when we overestimate its effectiveness. This winner's curse biases our estimates for selected options upward and can invalidate conventional confidence intervals. This article develops estimators and confidence intervals that eliminate this winner's curse. We illustrate our results by studying selection of job-training programs based on estimated earnings effects and selection of neighborhoods based on estimated economic opportunity. We find that our winner's curse corrections can make an economically significant difference to conclusions but still allow informative inference. [ABSTRACT FROM AUTHOR]

Based on some studies, there are many important parts of tool machines, all of which have some essential smaller-the-better-type quality characteristics. The six sigma quality index of the smaller-the-better type offers accurate measurement of the process yield and the six sigma quality level. In this paper, we first proposed a six sigma product index by integrating all evaluation indicators for products that contain several quality characteristics of the smaller-the-better type. Next, we derived the confidence interval of this six sigma product index and developed an evaluation model for product quality. When a product passes the evaluation of this model, not only can it be guaranteed that the product reaches the required quality level, but also a high rate of product yield can be ensured. In addition, we also created a product improvement testing model, which can avoid missing opportunities for improvement in the process to ensure improvement effects. This complete evaluation and improvement model is applicable to the entire machine tool industry chain. It can not only increase the product value of the machine tool industry chain but also decrease environmental pollution caused by rework or scrap, which is beneficial to companies to enhance their image of fulfilling social responsibilities. Apart from the above advantages, the model formed in this paper is based on confidence intervals, thereby reducing the chance of misjudgment resulting from sampling error. [ABSTRACT FROM AUTHOR]

A performance evaluation matrix (PEM) is an evaluation tool for assessing customer satisfaction and the importance of service items across various services. In addition, inferences based on point estimates of sample data can increase the risk of misjudgment due to sampling errors. Thus, this paper creates a decision-making model for a performance evaluation matrix based on upper confidence limits to provide various service operating systems for performance evaluation and decision making. The concept is that through the gap between customer satisfaction and the level of importance of each service item, we are able to identify critical-to-quality (CTQ) service items requiring improvement. Many studies have indicated that customer satisfaction and the importance of service items follow a beta distribution, and based on the two parameters of this distribution, the proposed indices for customer satisfaction and the importance of service items represent standardization. The vertical axis of a PEM represents the importance index; the horizontal axis represents the satisfaction index. Since these two indices have unknown parameters, this paper uses the upper confidence limit of the satisfaction index to find out the CTQ service items and the upper confidence limit of the importance index to determine the order of improvement priority for each service item. This paper then establishes a decision-making model for a PEM based on the above-mentioned decision-making rules. Since all decision-making rules proposed in this paper are established through upper confidence limits, the risk of misjudgment caused by sampling errors can be reduced. Finally, this article uses a practical example to illustrate how to use a PEM to find CTQ service items and determine the order of improvement priority for these service items that need to be improved. [ABSTRACT FROM AUTHOR]

This article describes three methods for carrying out nonasymptotic inference on partially identified parameters that are solutions to a class of optimization problems. Applications in which the optimization problems arise include estimation under shape restrictions, estimation of models of discrete games, and estimation based on grouped data. The partially identified parameters are characterized by restrictions that involve the unknown population means of observed random variables in addition to structural parameters. Inference consists of finding confidence intervals for functions of the structural parameters. Our theory provides finite-sample lower bounds on the coverage probabilities of the confidence intervals under three sets of assumptions of increasing strength. With the moderate sample sizes found in most economics applications, the bounds become tighter as the assumptions strengthen. We discuss estimation of population parameters that the bounds depend on and contrast our methods with alternative methods for obtaining confidence intervals for partially identified parameters. The results of Monte Carlo experiments and empirical examples illustrate the usefulness of our method. [ABSTRACT FROM AUTHOR]

Classical randomized experiments, equipped with randomization-based inference, provide assumption-free inference for treatment effects. They have been the gold standard for drawing causal inference and provide excellent internal validity. However, they have also been criticized for questionable external validity, in the sense that the conclusion may not generalize well to a larger population. The randomized survey experiment is a design tool that can help mitigate this concern, by randomly selecting the experimental units from the target population of interest. However, as pointed out by Morgan and Rubin, chance imbalances often exist in covariate distributions between different treatment groups even under completely randomized experiments. Not surprisingly, such covariate imbalances also occur in randomized survey experiments. Furthermore, the covariate imbalances happen not only between different treatment groups, but also between the sampled experimental units and the overall population of interest. In this article, we propose a two-stage rerandomization design that can actively avoid undesirable covariate imbalances at both the sampling and treatment assignment stages. We further develop asymptotic theory for rerandomized survey experiments, demonstrating that rerandomization provides better covariate balance, more precise treatment effect estimators, and shorter large-sample confidence intervals. We also propose covariate adjustment to deal with remaining covariate imbalances after rerandomization, showing that it can further improve both the sampling and estimated precision. Our work allows general relationship among covariates at the sampling, treatment assignment and analysis stages, and generalizes both rerandomization in classical randomized experiments and rejective sampling in survey sampling. [ABSTRACT FROM AUTHOR]

Heterogeneity in agents' preferences is generally analysed through mixed logit models, which assume taste parameters are distributed in the population according to a certain mixing distribution. As a result, if the utility function is linear in attributes, the willingness to pay is the ratio of two random parameters and is itself random. This paper proposes a technique built on the Delta method, partly analytical and partly based on simulations, to obtain the sampling distribution of the willingness to pay, accounting for both heterogeneity and sampling error. The paper contributes to the literature by: (i) redressing some imprecisions in Bliemer and Rose (2013) that produce biased results; (ii) proposing a faster estimation process, compared to the Krinsky and Robb (1986, 1990) method that, relying on simulation only, proves computationally more demanding; (iii) comparing the performance of different methods using both synthetic and real data sets. The paper shows, via a Monte Carlo study, that the method we develop and the Krinsky and Robb one produce similar results, while outperforming that proposed by Bliemer and Rose. • Uncertainty in estimating Willingness To Pay under Mixed Logit Model arises from both heterogeneity and sampling error. • Delta method can be used, in combination with normal mixtures, to estimate both sources of uncertainty. • Both confidence and prediction intervals can be computed for Willingness To Pay by means of Delta method. • Delta method, being partly analytical, proves time-saving when compared to Krinsky and Robb method. [ABSTRACT FROM AUTHOR]

As the Internet of Things (IoT) becomes more and more popular and full-grown, diverse technologies for measurement and collection of business data continually improve as well. Effective data analysis of and applications can be helpful to stores to make smart and quick decisions in a jiffy, so that the percentage of customer satisfaction and in-store shopping can increase to raise the total revenue. Some researchers have suggested that the number of customers who enter a store refers to a Poisson process. Based on previous research, an attribute service performance index was proposed in this paper. This paper reviewed the fuzzy one-tailed testing model of the attribute service performance index and put forward a fuzzy two-tailed testing model of two indices based on the confidence interval to verify whether the improvement had a significant effect. Now that this fuzzy evaluation model is built on the confidence interval of the index, we can diminish the chance of misjudgment caused by sampling error. Its design can incorporate the past data or expert experience. Thus, the evaluation accuracy can be retained in the case of small-sized samples. [ABSTRACT FROM AUTHOR]

It is important to estimate the sample data when inspecting the quality of products. Therefore, sampling error and uncertainty in the measurement are inevitable, which may lead to misjudgment in product performance evaluation. Since the important quality characteristics of gasoline belong to one-sided specifications, a one-sided specification capability index was proposed to evaluate whether the process capabilities of various quality characteristics of gasoline reach the required quality levels. The 100(1−α)% upper confidence limits of the index were obtained to ensure low producer's risk and reduce sampling errors. To deal with fuzzy data and limited sample sizes, a fuzzy testing model based on the 100(1−α)% upper confidence limits of the index was developed. A practice example of 95 unleaded gasoline was used to illustrate the effectiveness and usefulness of the proposed method. The result shows that two quality characteristics—Reid vapor pressure and oxygen content—of the nine quality characteristics of the 95 unleaded gasoline should be considered for improvements. This study provided an evaluation procedure to facilitate quality managers to take the opportunity to improve product quality, promoting the improvement of air quality, and the sustainability of industrial processes or products. [ABSTRACT FROM AUTHOR]

Statistical power analyses are used in the design of experiments to determine the required number of specimens, and thus the expenditure, of a test. Commonly, when analyzing and planning life tests of technical products, only the confidence level is taken into account for assessing uncertainty. However, due to the sampling error, the confidence interval estimation varies from test to test; therefore, the number of specimens needed to yield a successful reliability demonstration cannot be derived by this. In this paper, a procedure is presented that facilitates the integration of statistical power analysis into reliability demonstration test planning. The Probability of Test Success is introduced as a metric in order to place the statistical power in the context of life test planning of technical products. It contains the information concerning the probability that a life test is capable of demonstrating a required lifetime, reliability, and confidence. In turn, it enables the assessment and comparison of various life test types, such as success run, non-censored, and censored life tests. The main results are four calculation methods for the Probability of Test Success for various test scenarios: a general method which is capable of dealing with all possible scenarios, a calculation method mimicking the actual test procedure, and two analytic approaches for failure-free and failure-based tests which make use of the central limit theorem and asymptotic properties of several statistics, and therefore simplify the effort involved in planning life tests. The calculation methods are compared and their respective advantages and disadvantages worked out; furthermore, the scenarios in which each method is to be preferred are illustrated. The applicability of the developed procedure for planning reliability demonstration tests using the Probability of Test Success is additionally illustrated by a case study. [ABSTRACT FROM AUTHOR]

Differential privacy is a restriction on data processing algorithms that provides strong confidentiality guarantees for individual records in the data. However, research on proper statistical inference, that is, research on properly quantifying the uncertainty of the (noisy) sample estimate regarding the true value in the population, is currently still limited. This article proposes and evaluates several strategies to compute valid differentially private confidence intervals for the median. Instead of computing a differentially private point estimate and deriving its uncertainty, we directly estimate the interval bounds and discuss why this approach is superior if ensuring privacy is important. We also illustrate that addressing both sources of uncertainty—the error from sampling and the error from protecting the output—simultaneously should be preferred over simpler approaches that incorporate the uncertainty in a sequential fashion. We evaluate the performance of the different algorithms under various parameter settings in extensive simulation studies and demonstrate how the findings could be applied in practical settings using data from the 1940 Decennial Census. [ABSTRACT FROM AUTHOR]

We introduce a new method of estimating accepted species diversity by adapting mark-recapture methods to comparisons of taxonomic databases. A taxonomic database should become more complete over time, so the error bar on an estimate of its completeness and the known diversity of the taxon it treats will decrease. Independent databases can be correlated, so we use the time course of estimates comparing them to understand the effect of correlation. If a later estimate is significantly larger than an earlier one, the databases are positively correlated, if it is significantly smaller, they are negatively correlated, and if the estimate remains roughly constant, then the correlations have averaged out. We tested this method by estimating how complete MolluscaBase is for accepted names of terrestrial gastropods. Using random samples of names from an independent database, we determined whether each name led to a name accepted in MolluscaBase. A sample tested in August 2020 found that 16.7% of tested names were missing; one in July 2021 found 5.3% missing. MolluscaBase grew by almost 3,000 accepted species during this period, reaching 27,050 species. The estimates ranged from 28,409 ± 365 in 2021 to 29,063 ± 771 in 2020. All estimates had overlapping 95% confidence intervals, indicating that correlations between the databases did not cause significant problems. Uncertainty beyond sampling error added 475 ± 430 species, so our estimate for accepted terrestrial gastropods species at the end of 2021 is 28,895 ± 630 species. This estimate is more than 4,000 species higher than previous ones. The estimate does not account for ongoing flux of species into and out of synonymy, new discoveries, or changing taxonomic methods and concepts. The species naming curve for terrestrial gastropods is still far from reaching an asymptote, and combined with the additional uncertainties, this means that predicting how many more species might ultimately be recognized is presently not feasible. Our methods can be applied to estimate the total number of names of Recent mollusks (as opposed to names currently accepted), the known diversity of fossil mollusks, and known diversity in other phyla. [ABSTRACT FROM AUTHOR]

A rate ratio (RR) is an important metric for comparing cancer risks among different subpopulations. Inference for RR becomes complicated when populations used for calculating age-standardized cancer rates involve sampling errors, a situation that arises increasingly often when sample surveys must be used to obtain the population data. We compare a few strategies of estimating the standardized RR and propose bias-corrected ratio estimators as well as the corresponding variance estimators and confidence intervals that simultaneously consider the sampling error in estimating populations and the traditional Poisson error in the occurrence of cancer case or death. Performance of the proposed methods is evaluated empirically based on simulation studies. An application to immigration disparities in cancer mortality among Hispanic Americans is discussed. Our simulation studies show that a bias-corrected RR estimator performs the best in reducing the bias without increasing the coefficient of variation; the proposed variance estimators for the RR estimators and associated confidence intervals are fairly accurate. Finding of our application study are both interesting and consistent with the common sense as well as the results of our simulation studies. [ABSTRACT FROM AUTHOR]

Numerous studies have pointed out that the issue of global warming is getting increasingly more serious. Therefore, the concepts of circular economy (CE) and sharing economy have been more and more valued by enterprises and governments. With the gradual popularization and maturity of the Internet of Things (IoT), various smart APP platforms have sprung up rapidly. For example, the fuzzy evaluation model of bank APP performance was proposed in such an environment, aiming to improve the APP service performance by means of evaluating, analyzing, improving, and enhancing customers' satisfaction with their use of APPs, and increasing the number of users of APPs. Since the follow-up of the article did not mention the improved testing model used to verify the improvement effect, this paper then proposed a fuzzy two-tailed testing model with two indices before and after the improvement based on the confidence interval to verify whether the improvement has had a significant effect. This complete bank APP fuzzy performance evaluation, analysis, and improvement model measured the bank APP operation performance using customer time intervals, so the data collection time was short. Not only can it meet enterprises' need for rapid response and grasp the opportunity for improvement to achieve the effect of energy-saving and carbon reduction, but it also can satisfy enterprises' requirement to pursue fast and accurate decision-making. Furthermore, the fuzzy two-tailed test proposed by this paper was based on the confidence interval, which can reduce the risk of misjudgment caused by sampling error. Plenty of studies have indicated that the designs based on confidence intervals can integrate expert experience and past data so that the accuracy of testing can be maintained in the case of small-sized samples. [ABSTRACT FROM AUTHOR]

The operating performance index (OPI) was developed by Chen and Yang (J Comput Appl Math 343:737–747, 2018) from the Six Sigma process quality index. The fact that OPIs include unknown parameters means that they must be formulated using estimates based on sample data. Unfortunately, cost and effectiveness considerations in practice have led to sample size limitation and measurement uncertainty. In this study, we sought to enhance testing accuracy and overcome the uncertainties in measurement by applying confidence intervals of OPI to derive a fuzzy number and membership function for OPI. We developed a one-tailed fuzzy test method to determine whether performance reaches the required level. We also developed a two-tailed fuzzy testing method based on two OPIs to serve as a verification model for the effectiveness of improvement measures. Both fuzzy testing methods are proposed based on confidence intervals of the indices to reduce the risk of misjudgment caused by sampling errors and enhance testing accuracy. [ABSTRACT FROM AUTHOR]

Industry 4.0 has fostered innovation in industries around the world. Manufacturing industries in particular are advancing towards smart manufacturing by integrating and applying relevant technologies. The output value of machine tools in Taiwan is among the top of the world and the central region is a key area for this industry chain, which supplies manufacturers in Taiwan and their international downstream customers. To support innovation in this industry, the current study used the Six Sigma quality indices for smaller-the-better, larger-the-better, and nominal-the-best quality characteristics to construct a fuzzy decision-making model. Based on this model, we propose a process quality fuzzy analysis chart (PQFAC) for process quality improvement. Our use of fuzzy decision values to replace lower confidence limits decreases the probability of misjudgment made by sampling errors. The proposed fuzzy model also offers a more accurate assessment of process improvement requirements. We provide a real-world example to demonstrate the applicability of the proposed approach. Machine tool manufacturers can apply the platform and proposed model to evaluate their process capabilities for the vital parts suppliers and downstream customers, determine optimal machine parameter settings for processes with inadequate accuracy or precision, establish more suitable machine repair and maintenance systems, and combine the improvement experiences of customers to create an improvement knowledge base. This will enhance product value and industry competitiveness for the entire machine tool industry chain. [ABSTRACT FROM AUTHOR]

We consider partially observed binary matched-pair data. We assume that the incomplete subjects are missing at random. Within this missing framework, we propose an EM-algorithm based approach to construct an interval estimator of the proportion difference incorporating all the subjects. In conjunction with our proposed method, we also present two improvements to the interval estimator through some correction factors. The performances of the three competing methods are then evaluated through extensive simulation. Recommendation for the method is given based on the ability to preserve type-I error for various sample sizes. Finally, the methods are illustrated in two real-world data sets. An R-function is developed to implement the three proposed methods. [ABSTRACT FROM AUTHOR]

Different sampling methods can be used in forest surveys. It is important to know the precision and accuracy of these sampling methods, and which one is the most appropriate in specific conditions of the forest population. The aim of this study was to compare estimates of a forest inventory performed by different sampling methods with forest census results. The sampling methods evaluated were the fixed-area method and the variable-area methods of Bitterlich, Prodan, and Strand. The data were obtained in a 15-year-old thinned stand of Pinus taeda L., located in the municipality of Teixeira Soares, southern Brazil, with a total area of 12.80 ha. Initially, the forest census was carried out, and subsequently, the sample units for each sampling method were distributed in the stand, with a common starting point. The variables used to compare the sample results with the census means were quadratic diameter, number of trees, basal area, and volume, per hectare. Precision and accuracy were evaluated by sampling error and whether the confidence intervals covered the population means, respectively. The fixed-area and Bitterlich methods stood out in precision for all variables analysed. The fixedarea, Bitterlich and Strand methods with proportion to height provided more accurate estimates. The Prodan method provided inaccurate and imprecise estimates for the variables under analysis, except for the quadratic diameter. [ABSTRACT FROM AUTHOR]

Copyright of Texto & Contexto Enfermagem is the property of Universidade Federal de Santa Catarina, Programa de Pos-Graduacao de Enfermagem and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The article provides understanding of the most important information that clinicians need to know about meta-analyses. Topics discussed are dispersion of true effects of size and dispersion secondary to sampling error, equation for the prediction interval and its use in the practice of clinical medicine as well as in choosing among treatments, and distinction of prediction from confidence interval.

Accurate characterization of soil contaminant concentrations is often crucial for assessing risks to human and ecological health. However, fine-scale assessments of large tracts of land can be cost prohibitive due to the number of samples needed. One solution to this problem is to extrapolate sampling results from one area to another unsampled area. In the absence of a validated extrapolation methodology, regulatory agencies have employed policy-based techniques for large sites, but the likelihood of decision errors resulting from these extrapolations is largely unexplored. This study describes the results of a simulation study aimed at guiding environmental sampling for sites where extrapolation concepts are of interest. The objective of this study is to provide practical recommendations to regulatory agencies for extrapolating sampling results on large tracts of land while minimizing errors that are detrimental to human health. A variety of site investigation scenarios representative of environmental conditions and sampling schemes were tested using adaptive sampling when collecting discrete samples or applying incremental sampling methodology (ISM). These simulations address extrapolation uncertainty in cases where a Pilot Study might result in either false noncompliance or false compliance conclusions. A wide range of plausible scenarios were used that reflect the variety of heterogeneity seen at large sites. This simulation study demonstrates that ISM can be reliably applied in a Pilot Study for purposes of extrapolating the outcome to a large area site because it decreases the likelihood of false non-compliance errors while also providing reliable estimates of true compliance across unsampled areas. The results demonstrate how errors depend on the magnitude of the 95% upper confidence limit for the mean concentration (95UCL) relative to the applicable action level, and that error rates are highest when the 95UCL is within 10%–40% of the action level. The false compliance rate can be reduced to less than 5% when 30% or more of the site is characterized with ISM. False compliance error rates using ISM are insensitive to the fraction of the decision units (DUs) that are characterized with three replicates (with a minimum of 10 percent), so long as 95UCLs are calculated for the DUs with one replicate using the average coefficient of variation from the three replicate DUs. • Environmental assessments of large tracts of land often use extrapolation methods. • Simulations support the use of extrapolation for the protection of human health. • An average coefficient of variation predicts upper end concentrations. • Using discrete sampling, 30% of the site must be characterized before extrapolation. • Incremental sampling requires 10% site characterization before extrapolation. [ABSTRACT FROM AUTHOR]

Microplastics (MPs), plastic particles <5 mm in diameter, are emerging ubiquitous pollutants in natural environments, including freshwater ecosystems. As rivers facilitate efficient transport among landscapes, monitoring is crucial for elucidating the origin, dynamics, and fate of MPs. However, standardized methodologies for in situ sampling in freshwater environments remain undefined to date. Specifically, evaluating the sampling error of MP concentration estimates is crucial for comparing results among studies. This study proposes a novel method for computing confidence intervals (CIs) from a single estimate of numerical concentration (expressed in particles·m−3). MPs are expected to disperse according to purely random processes, such as turbulent diffusion, and to consequently exhibit a random distribution pattern that follows a Poisson point process. Accordingly, the present study introduced a framework based on the Poisson point process to compute CIs, which were validated using MP samples from two urban rivers in Chiba, Japan, obtained using a mesh with an opening size of 335 μm. Random number simulations revealed that the CIs were applicable when ≥10 MPs were present in a sample. Further, when ≥50 MPs were present in a sample, the sampling error (95% CI) was within ±30% of the concentration estimates. The proposed framework allows for the intercomparison of single river MP samples despite the lack of sample replicates. Further, the present study emphasizes that the volume of sampled river water is the only controllable parameter that can reduce the sampling error. [Display omitted] • Assuming Poisson process allows computation of CIs for single MP samplings. • Collecting ≥50 MPs allows 95% CI within ±30% of concentration estimate. • Sample water volume is the only controllable parameter to reduce sampling error. [ABSTRACT FROM AUTHOR]

• TCATA data explored and visualized using PCA. • Bootstrap procedures used to investigate uncertainty in scores. • Uncertainty in scores visualized in different ways. • Index proposed to evaluate discriminability of scores. • New graphical features proposed for PCA biplots. Temporal check-all-that-apply (TCATA) data can be summarized and explored using principal component analysis (PCA). Here we analyze TCATA data on Syrah wines obtained from a trained sensory panel. We evaluate new and existing methods to explore the uncertainty in the PCA scores. To do so, we use the bootstrap procedure to obtain many virtual panels from the real panel's data. Virtual-panel PCA scores are obtained using two methods. The first method, called the partial bootstrap (PB), obtains virtual-panel scores from regression. The second method, called the truncated total bootstrap (TTB), applies PCA to the virtual-panel results to obtain scores, which are truncated and superimposed on the real-panel scores by Procrustes rotation. We use the virtual scores from each method to investigate uncertainty in the real-panel PCA scores visually and numerically. To understand the uncertainty of the scores, we obtain confidence ellipses (CEs) and their areas, as well as confidence intervals (CIs) and their widths. Next, to determine whether PCA scores for different samples are well separated, we propose a procedure for approximating the standard errors of sample differences and correcting for multiple comparisons. We propose a discriminability index, and show that it can enhance the interpretability of PCA results. We incorporate graphical features into our PCA biplots to visualize discriminability. We did not find a large difference between the PB and TTB methods for understanding the uncertainty and discriminability in PCA scores. Although the TCATA data that we analyzed have a special structure, the methodological approaches presented here can be readily adapted to other applications of PCA. [ABSTRACT FROM AUTHOR]

• A novel PCAC to measure products with multi-quality characteristic. • Pareto optimality to achieve the performance optimization for CM selection. • A feedback mechanism to advise ineligible CMs on quality issues. • A rigid coupling to validate the proposed methodology. Outsourcing is a crucial strategy of the mechanical manufacturing industry. When outsourcing, it is necessary for companies to carefully inspect the performance of contract manufacturers (CMs) to ensure high-quality products and satisfactory services. This study presents an integrated methodology for the quality performance assessment and optimization of products with multiple quality characteristics for CM selection in the mechanical manufacturing industry. First, we present a novel process capability analysis chart (PCAC) using the 100(1– α)% upper confidence limits of C pmh , C puh , and C plh to gauge the process capabilities of products with multiple quality characteristics and reduce the influence of sampling errors. Second, we apply Pareto optimality to reexamine eligible CMs under the objectives of maximizing performance in individual quality characteristics and minimizing variance in overall performance. A feedback mechanism is included to advise ineligible CMs on means of improvement. Finally, we present a case study to demonstrate the feasibility and effectiveness of the proposed methodology. [ABSTRACT FROM AUTHOR]