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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]

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]

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]

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]

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]

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]

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]

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]

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]

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.

The present study was conducted to determine the extent of observation of patients' privacy by physicians and nurses and its relationship with patient satisfaction. This descriptive correlational study was conducted on 600 patients selected by convenience sampling. Based on the patients' points of view, the level of observation of patients' privacy and its dimensions, especially the psychosocial dimension, were reported to be higher in nurses than in physicians. Pearson's correlation coefficient showed a direct and significant relationship between the observation of privacy by the nurses and physicians and different dimensions of patient satisfaction. [ABSTRACT FROM AUTHOR]

Cohen's kappa coefficient was originally proposed for two raters only, and it later extended to an arbitrarily large number of raters to become what is known as Fleiss' generalized kappa. Fleiss' generalized kappa and its large-sample variance are still widely used by researchers and were implemented in several software packages, including, among others, SPSS and the R package "rel." The purpose of this article is to show that the large-sample variance of Fleiss' generalized kappa is systematically being misused, is invalid as a precision measure for kappa, and cannot be used for constructing confidence intervals. A general-purpose variance expression is proposed, which can be used in any statistical inference procedure. A Monte-Carlo experiment is presented, showing the validity of the new variance estimation procedure. [ABSTRACT FROM AUTHOR]

Objective: Orthorexia Nervosa is a new eating disorder and is known as an excessive control of quality of the eaten foods. During postpartum period, related to the physiological and medical changes, it was stated that most of the women have concerns about their body image and therefore they have tendency to change their lifestyle, and it can lead mothers to Orthorexia Nervosa. The aim of this study was to assess the Orthorexia Nervosa tendencies of postpartum women and investigate the related factors. Methods: This descriptive study was carried out among postpartum women between 1st December 2018-1st February 2019. We contacted with the women via e-mails through a social media group special for postpartum women which had 10.350 members at the time of study. The minimum sample size for universe was estimated as 370 women, assuming 95% confidence interval and 5% sampling error. The questionnaire consists of two parts: the general features of participants and the ORTO-11 questionnaire. Results: The mean ORTO-11 scale score of all participants (N=511) was 22.68±4.09 (min=12; max=35) and had statistically significant relationship with age, working status, vocation, family style, the understanding of being healthy, physical activity, diet status and the order of nutrition status. According to cut-off point, 87.7 % (n=426) of the participants were found to be at risk of developing Orthorexia Nervosa. Conclusions: The tendency toward Orthorexia Nervosa was greater among mothers in postpartum period. Also the mothers who change their eating habits and change the physical activity status after delivery had higher ON tendency than others. So the postpartum period is very important to follow up the mothers about ON and such eating disorders because of the changing lifestyle habits. Family physicians have a critical role in this regard with their preventive medicine qualifications. [ABSTRACT FROM AUTHOR]

This study develops a theoretical model for the costs of an exam as a function of its duration. Two kind of costs are distinguished: (1) the costs of measurement errors and (2) the costs of the measurement. Both costs are expressed in time of the student. Based on a classical test theory model, enriched with assumptions on the context, the costs of the exam can be expressed as a function of various parameters, including the duration of the exam. It is shown that these costs can be minimized in time. Applied in a real example with reliability.80, the outcome is that the optimal exam time would be much shorter and would have reliability.675. The consequences of the model are investigated and discussed. One of the consequences is that optimal exam duration depends on the study load of the course, all other things being equal. It is argued that it is worthwhile to investigate empirically how much time students spend on preparing for resits. Six variants of the model are distinguished, which differ in their weights of the errors and in the way grades affect how much time students study for the resit. [ABSTRACT FROM AUTHOR]

Many corporations purchase components from suppliers, which can reduce operating costs and enable firms to focus their resources on core advantages. Studies have indicated that process quality and manufacturing time performance are two crucial indicators for supplier selection. We used the process quality index and a manufacturing time performance index to create a dual dimensional fuzzy supplier selection model. First, the upper confidence limits of these two indices were derived, and a fuzzy membership function based on these limits was constructed. Based on the fuzzy test rules for process quality and manufacturing time performance, we divided the fuzzy supplier selection matrix into nine evaluation zones. Using the upper confidence limits of these two indices, we created evaluation coordinates and assigned weights based on the location of the coordinates. Then, the total of all the weights was employed to form a supplier selection index for which a higher value means a higher ranking. The use of confidence limits decreased the chance of misjudgment resulting from sampling errors while the fuzzy test rules increased the applicability of the model. Consequently, the proposed model can be used to select suppliers efficiently so as to form partnerships in which corporations and suppliers can grow together. [ABSTRACT FROM AUTHOR]

The stochastic Richardson extrapolation-based numerical error quantification (StREEQ) technique has been applied to accomplish a code verification for the cavity systemgenerated electromagnetic pulse (SGEMP) simulation code LASER-SGEMP. Here, the grid convergence index method estimates the discretization error caused by the finite difference, while the bootstrap sampling demonstrates the sampling error arising from the inherent stochastic noise. The electric field waveforms obtained by the LASER-SGEMP code agree well with the high precision solution from a reference. According to the StREEQ method, the convergence value of the electric field at 1.8 ns is calculated to be 0.955 V/m and the numerical error characterized by the 95% confidence interval is [0.948, 0.964] V/m, while the high precision solution is 0.961 V/m. Therefore, the code verification has supported the accuracy of the LASER-SGEMP code, and the StREEQ technique is proved to be capable of estimating the numerical error of the cavity SGEMP simulation. [ABSTRACT FROM AUTHOR]

Objectives: Health system responsiveness is a complicated issue that guides researchers in determining an efficient methodology to enhance the understanding of health care systems' perspectives. This study examined the relationship between patients' experience profiles and their satisfaction with medical outcomes. Design: The authors used 11 items from the Taiwanese Annual National Health Insurance survey and used latent class analysis (LCA) to develop experience profiles for 2012 Traditional Chinese Medicine (TCM) patients. A logistic regression model was developed to explore differences in patients' satisfaction with their treatment outcome across four groups identified using the LCA, with adjustment for demographic factors. Subjects: Patients' experiences with medical services in TCM in 2015. Outcome measures: Patients' satisfaction with their treatment outcome. Results: Participants (N = 2012) were divided into four groups. Regardless of gender and age, Group 2 (nall) held the lowest satisfaction with treatment outcome relative to those reported by the other three groups (odds ratios with p-value: Group 1 [pall]: 7.40, Group 3 [nComm]: 1.37, Group 4 [Skip]: 2.20, p < 0.001). Respondents with a more favorable patient experience reported higher satisfaction with treatment outcome. Conclusions: An increased favorable treatment experience in TCM (such as positive accessibility and better interpersonal relationships with providers) is associated with higher satisfaction with treatment outcome. The World Health Organization emphasizes that traditional medicine integrated with Western medicine can play an important role in achieving the goal of "Health for All." Health authorities should develop strategies aimed at enhancing patients' experiences in TCM to contribute to a positive care process. [ABSTRACT FROM AUTHOR]

Nonresponse is a potential source of errors in sample surveys. It introduces bias and large variance in the estimation of finite population parameters. Regression models have been recognized as one of the techniques of reducing bias and variance due to random nonresponse using auxiliary data. In this study, it is assumed that random nonresponse occurs in the survey variable in the second stage of cluster sampling, assuming full auxiliary information is available throughout. Auxiliary information is used at the estimation stage via a regression model to address the problem of random nonresponse. In particular, auxiliary information is used via an improved Nadaraya–Watson kernel regression technique to compensate for random nonresponse. The asymptotic bias and mean squared error of the estimator proposed are derived. Besides, a simulation study conducted indicates that the proposed estimator has smaller values of the bias and smaller mean squared error values compared to existing estimators of a finite population mean. The proposed estimator is also shown to have tighter confidence interval lengths at 95 % coverage rate. The results obtained in this study are useful for instance in choosing efficient estimators of a finite population mean in demographic sample surveys. [ABSTRACT FROM AUTHOR]

In the analysis of survey data, it is of interest to estimate and quantify uncertainty about means or totals for each of several nonoverlapping subpopulations or areas. When the sample size for a given area is small, standard confidence intervals based on data only from that area can be unacceptably wide. In order to reduce interval width, practitioners often utilize multilevel models in order to borrow information across areas, resulting in intervals centered around shrinkage estimators. However, such intervals only have the nominal coverage rate on average across areas under the assumed model for across-area heterogeneity. The coverage rate for a given area depends on the actual value of the area mean and can be nearly zero for areas with means that are far from the across-group average. As such, the use of uncertainty intervals centered around shrinkage estimators are inappropriate when area-specific coverage rates are desired. In this article, we propose an alternative confidence interval procedure for area means and totals under normally distributed sampling errors. This procedure not only has constant 1 − α frequentist coverage for all values of the target quantity but also uses auxiliary information to borrow information across areas. Because of this, the corresponding intervals have shorter expected lengths than standard confidence intervals centered on the unbiased direct estimator. Importantly, the coverage of the procedure does not depend on the assumed model for across-area heterogeneity. Rather, improvements to the model for across-area heterogeneity result in reduced expected interval width. [ABSTRACT FROM AUTHOR]

As the Internet-of-Things matures, technologies for the measurement and collection of production data are also improving. What is needed next is an effective information analysis model to aid in the timely adjustment of manufacturing parameters to optimize production. Production data analysis models must be continuously and properly utilized to monitor and maintain process quality. Improving product quality helps to lengthen service life, decrease scrap and rework, and reduce the social losses caused by malfunctions and maintenance. The Taguchi capability index Cpm can fully reflect the losses and yield of processes and is a convenient and effective tool to evaluate and analyze process data in the industry. As it contains unknown parameters, we derived the upper confidence limit (UCL) of Cpm based on collected production data. Due to the fuzzy uncertainties that are common in measurement data, we then used the UCL of the index to construct a fuzzy membership function and propose a fuzzy testing decision-making model to determine whether processes are in need of improvement. Before the proposed fuzzy test methods became full-fledged, we used the concept of sample size and the rules of statistical testing to explain the motivation underlying those methods. In fact, the sample size influences the risk of misjudgment in UCL, and in practice, sample sizes are rarely large due to cost and time considerations, thereby they produce larger UCL with a corresponding decrease in accuracy and increase in risk of misjudgment. The fuzzy test methods proposed in this study are based on statistical inference, and judgement is aided by expertise, thus are capable of solving the problems associated with larger UCL. Therefore, the theoretical foundation of this fuzzy testing decision-making model is the UCL, it can lower the chance of misjudgment caused by sampling errors and increase evaluation accuracy. [ABSTRACT FROM AUTHOR]

This paper proposes an operating performance index (OPI) based directly on the Six Sigma process quality index. We considered the following case: the number of customers arriving at a store follows a Poisson process of rate λ and the sequence of inter-arrival times is an exponential random variable with mean τ , where τ = 1/ λ. In operating performance assessments, using the statistical testing to evaluate the OPI can lower the risk of misjudgment caused by sampling error. A smaller sample size entails a larger sampling error, while a larger sample size entails a smaller sampling error. Thus, using critical value for statistical testing can result in inconsistencies for different sample size. We therefore referred to the one-tailed fuzzy method proposed by Buckley (2005) for the parameters of population distributions and developed a two-tailed fuzzy test for the OPI to assess operating performance. The advantage of this approach is that conventional measurement methods can be used during data collection, and then the confidence interval of the OPI can be used to construct a fuzzy membership function for fuzzy testing. This not only lowers the risk of misjudgment caused by sampling error, but also enhances testing accuracy. [ABSTRACT FROM AUTHOR]

Introduction: The promotion of a positive birth experience has been a main goal of the World Health Organization's (WHO) recent work on improving maternity care. The purpose of this study was to assess the cesarean rates, the prevalence of birth practices, perinatal outcomes, and maternal satisfaction, in women involved with the respectful maternity care (RMC) support groups in Sao Paulo, Brazil. Methods: This was a cross‐sectional study of women with low‐risk pregnancies who were assisted by professionals recommended by the RMC groups. An online questionnaire was administered. Variables to assess birth practices were classified as positive, negative, or unspecified according to the WHO guidelines. The Pearson chi‐square tests and odds ratios (ORs) with their corresponding 95% confidence intervals (CIs) were computed to assess differences between the groups. Results: Five‐hundred and eighty women completed the questionnaire. The cesarean rate was 14.7%, and the operative vaginal birth rate was 9.5%. The VBAC rate was 87.1%, and there was no significant difference in risk for cesarean between women with or without a prior cesarean. Of all women, 83.1% had a midwife's assistance and 75.5% hired a doula; 81.4% gave birth in a nonlithotomic position. The practices of enema, fasting and episiotomy were all under 2%. All 5‐minute Apgar scores were ≥7. Most (83.1%) women reported having a positive birth experience. Conclusions: Woman's engagement with the birth support groups and a transdisciplinary team focused on RMC are key elements to achieve positive perinatal outcomes and high women's satisfaction. [ABSTRACT FROM AUTHOR]

Evaluating the importance and the strength of empirical evidence requires asking three questions: First, what are the practical implications of the findings? Second, how precise are the estimates? Confidence intervals provide an intuitive way to communicate precision. Although nontechnical audiences often misinterpret confidence intervals (CIs), I argue that the result is less dangerous than the misunderstandings that arise from hypothesis tests. Third, is the model correctly specified? The validity of point estimates and CIs depends on the soundness of the underlying model. [ABSTRACT FROM AUTHOR]

This pilot study was conducted using a sample of 374 Portuguese occupational therapists to evaluate burnout levels and prevalence among occupational therapists as well as to relate those levels to practitioner age, gender, client age, years of professional activity, and area of practice. The Copenhagen Burnout Inventory questionnaire (Portuguese version) and a sociodemographic questionnaire was used. Results showed that ∼23%, 44%, and 45% of occupational therapists presented with client-related burnout, personal burnout (PB), and work-related burnout, respectively. Higher rates of burnout were observed across all dimensions as the age of the professionals increased, with more years of working increased the client-rated rate, and client age increased the PB rate. Outcomes suggest a need to implement intervention programs to promote personal and organizational strategies to prevent burnout. [ABSTRACT FROM AUTHOR]

Background: Adolescence and young adulthood carry risk for suicidal thoughts and behaviours (STB). An increasing subpopulation of young people consists of college students. STB prevalence estimates among college students vary widely, precluding a validated point of reference. In addition, little is known on predictors for between-study heterogeneity in STB prevalence. Methods: A systematic literature search identified 36 college student samples that were assessed for STB outcomes, representing a total of 634 662 students [median sample size = 2082 (IQR 353-5200); median response rate = 74% (IQR 37-89%)]. We used random-effects meta-analyses to obtain pooled STB prevalence estimates, and multivariate metaregression models to identify predictors of between-study heterogeneity. Results: Pooled prevalence estimates of lifetime suicidal ideation, plans, and attempts were 22.3% [95% confidence interval (CI) 19.5-25.3%], 6.1% (95% CI 4.8-7.7%), and 3.2% (95% CI 2.2-4.5%), respectively. For 12-month prevalence, this was 10.6% (95% CI 9.1-12.3%), 3.0% (95% CI 2.1-4.0%), and 1.2% (95% CI 0.8-1.6%), respectively. Measures of heterogeneity were high for all outcomes (I2 = 93.2-99.9%), indicating substantial between-study heterogeneity not due to sampling error. Pooled estimates were generally higher for females, as compared with males (risk ratios in the range 1.12-1.67). Higher STB estimates were also found in samples with lower response rates, when using broad definitions of suicidality, and in samples from Asia. Conclusions: Based on the currently available evidence, STB seem to be common among college students. Future studies should: (1) incorporate refusal conversion strategies to obtain adequate response rates, and (2) use more fine-grained measures to assess suicidal ideation. [ABSTRACT FROM AUTHOR]

The usefulness of biodiversity indicators strongly increases if accompanied by measures of uncertainty. In the case of indicators that combine population indices of species, however, the inclusion of the uncertainty of the species indices has shown to be hard to realize, usually due to imperfections in monitoring programmes. Missing values and time series of different lengths preclude the use of analytical approaches, whereas bootstrapping across sites requires the raw abundance data on the site level, which may not always be available. Sometimes bootstrapping across species rather than sites is opted for, but this approach ignores the uncertainty attached to species indices. We developed a method to account for sampling error of species indices in the calculation of multi-species indicators based on Monte Carlo simulation of annual species indices. The construction of confidence intervals enables various trend assessments, like testing for linear or smooth trends, testing for changes between two time points, testing the significance of a suspected change-point and testing for differences between two multi-species indicators. Here, we compare our method with conventional methods and illustrate the benefits of our approach using Dutch breeding bird indicators. [ABSTRACT FROM AUTHOR]

Reliable measurements are key to social science research. Multiple measures of reliability of the total score have been developed, including coefficient alpha, coefficient omega, the greatest lower bound reliability, and others. Among these, the coefficient alpha has been most widely used, and it is reported in nearly every study involving the measure of a construct through multiple items in social and behavioral research. However, it is known that coefficient alpha underestimates the true reliability unless the items are tau-equivalent, and coefficient omega is deemed as a practical alternative to coefficient alpha in estimating measurement reliability of the total score. However, many researchers noticed that the difference between alpha and omega is minor in applications. Since the observed differences in alpha and omega can be due to sampling errors, the purpose of the present study, therefore, is to propose a method to evaluate the difference of coefficient alpha ( α ^ ) and omega ( ω ^ ) statistically. In particular, the current article develops a procedure to estimate the SE of ( ω ^ − α ^ ) and consequently the confidence interval (CI) for ( ω − α ). This procedure allows us to test whether the observed difference ( ω ^ − α ^ ) is due to sample error or ω ^ is significantly greater than α ^ . The developed procedure is then applied to multiple real data sets from well-known scales to empirically verify the values of ( ω ^ − α ^ ) in practice. Results showed that in most of the comparisons the differences are significantly above zero but cases also exist where the CIs contain zero. An R program for calculating ω ^ , α ^ , and the SE of ( ω ^ − α ^ ) is also included in the present study so that the developed procedure is easily accessible to applied researchers. [ABSTRACT FROM AUTHOR]

The American Community Survey (ACS) provides valuable, timely population estimates but with increased levels of sampling error. Although the margin of error is included with aggregate estimates, it has not been incorporated into segregation indexes. With the increasing levels of diversity in small and large places throughout the United States comes a need to track accurately and study changes in racial and ethnic segregation between censuses. The 2005-2009 ACS is used to calculate three dissimilarity indexes (D) for all core-based statistical areas (CBSAs) in the United States. We introduce a simulation method for computing segregation indexes and examine them with particular regard to the size of the CBSAs. Additionally, a subset of CBSAs is used to explore how ACS indexes differ from those computed using the 2000 and 2010 censuses. Findings suggest that the precision and accuracy of D from the ACS is influenced by a number of factors, including the number of tracts and minority population size. For smaller areas, point estimates systematically overstate actual levels of segregation, and large confidence intervals lead to limited statistical power. [ABSTRACT FROM AUTHOR]

A challenge when interpreting replications is determining whether the results of a replication “successfully” replicate the original study. Looking for consistency between two studies is challenging because individual studies are susceptible to many sources of error that can cause study results to deviate from each other and the population effect in unpredictable directions and magnitudes. In the current paper, we derive methods to compute a prediction interval, a range of results that can be expected in a replication due to chance (i.e., sampling error), for means and commonly used indexes of effect size: correlations and d-values. The prediction interval is calculable based on objective study characteristics (i.e., effect size of the original study and sample sizes of the original study and planned replication) even when sample sizes across studies are unequal. The prediction interval provides an a priori method for assessing if the difference between an original and replication result is consistent with what can be expected due to sample error alone. We provide open-source software tools that allow researchers, reviewers, replicators, and editors to easily calculate prediction intervals. [ABSTRACT FROM AUTHOR]

Background:The use of the borderline regression method (BRM) is a widely accepted standard setting method for OSCEs. However, it is unclear whether this method is appropriate for use with small cohorts (e.g. specialist post-graduate examinations). Aims and methods:This work uses an innovative application of resampling methods applied to four pre-existing OSCE data sets (number of stations between 17 and 21) from two institutions to investigate how the robustness of the BRM changes as the cohort size varies. Using a variety of metrics, the ‘quality’ of an OSCE is evaluated for cohorts of approximatelyn = 300 down ton = 15. Estimates of the standard error in station-level and overall pass marks,R2coefficient, and Cronbach’s alpha are all calculated as cohort size varies. Results and conclusion: For larger cohorts (n > 200), the standard error in the overall pass mark is small (less than 0.5%), and for individual stations is of the order of 1–2%. These errors grow as the sample size reduces, with cohorts of less than 50 candidates showing unacceptably large standard error. Alpha andR2also become unstable for small cohorts. The resampling methodology is shown to be robust and has the potential to be more widely applied in standard setting and medical assessment quality assurance and research. [ABSTRACT FROM PUBLISHER]

Background: Propensity score methods have become a popular tool for reducing selection bias in making causal inference from observational studies in medical research. Propensity score matching, a key component of propensity score methods, normally matches units based on the distance between point estimates of the propensity scores. The problem with this technique is that it is difficult to establish a sensible criterion to evaluate the closeness of matched units without knowing estimation errors of the propensity scores. Methods: The present study introduces interval matching using bootstrap confidence intervals for accommodating estimation errors of propensity scores. In interval matching, if the confidence interval of a unit in the treatment group overlaps with that of one or more units in the comparison group, they are considered as matched units. Results: The procedure of interval matching is illustrated in an empirical example using a real-life dataset from the Nursing Home Compare, a national survey conducted by the Centers for Medicare and Medicaid Services. The empirical example provided promising evidence that interval matching reduced more selection bias than did commonly used matching methods including the rival method, caliper matching. Interval matching's approach methodologically sounds more meaningful than its competing matching methods because interval matching develop a more "scientific" criterion for matching units using confidence intervals. Conclusions: Interval matching is a promisingly better alternative tool for reducing selection bias in making causal inference from observational studies, especially useful in secondary data analysis on national databases such as the Centers for Medicare and Medicaid Services data. [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]

The authors express their views on an article by Ian McKeague and Min Qian on statistical research that is published in this issue. Topics discussed include the cumulative distribution function (c.d.f.) of the estimation error; estimation error when testing a null hypothesis; and confidence interval mentioned in the article that is obtained through the limit distribution from Theorem 1.

Numerous key components of tool machines possess critical smaller-the-better-type quality characteristics. Under the assumption of normality, a one-to-one mathematical relationship exists between the process quality index and the process yield. Therefore, this paper utilized the index to produce a quality fuzzy evaluation model aimed at the small-the-better-type quality characteristics and adopted the model as a decision-making basis for improvement. First, we derived the 100(1 − α)% confidence region of the process mean and process standard deviation. Next, we obtained the 100(1 − α)% confidence interval of the quality index using the mathematical programming method. Furthermore, a one-tailed fuzzy testing method based on this confidence interval was proposed, aiming to assess the process quality. In addition, enterprises' pursuit of rapid response often results in small sample sizes. Since the evaluation model is built on the basis of the confidence interval, not only can it diminish the risk of wrong judgment due to sampling errors, but it also can enhance the accuracy of evaluations for small sample sizes. [ABSTRACT FROM AUTHOR]

High fidelity computational fluid dynamics simulations of ship airwakes are often performed with time accurate, turbulence resolving methods, such as large eddy simulation or detached eddy simulation. In our review of the literature we find that the finite sample error in the results of these simulations is rarely expressed in terms of uncertainty in the statistics. This makes it difficult to determine if any disagreement with experiment or other simulations can be attributed to finite sample time, grid resolution, or modelling approximations. In this paper, turbulence resolving simulations of the airwake over the SFS1 geometry are used to demonstrate a method for quantifying the uncertainty due to finite sample error with an estimated confidence interval. Based on this quantification, a stopping criterion is then formulated so that the simulation time can be set by a predetermined requirement for the confidence in the statistics. [Display omitted] • A comprehensive review of the literature on CFD simulations of ship airwakes is presented. • The dependence of velocity spectra on grid resolution in ship airwake simulations is studied. • A method for estimating the confidence intervals for flow statistics from ship airwake simulations is formulated. • A stopping criterion based on estimated confidence interval widths is proposed. • A concise set of recommendations for grid resolutions, time steps, and simulation lengths for ship airwake CFD is made. [ABSTRACT FROM AUTHOR]

When all of the one-sided specification indices of each quality characteristic reach the requirements of the process quality level, they can ensure that the process capability of the product meets the requirements of the process quality level. This study constructs a fuzzy membership function based on the upper confidence limit of the index, derives the fuzzy critical value, and then labels the fuzzy critical value on the axis of the visualized radar chart as well as connects adjacent critical points to shape a regular polygonal critical region. Next, this study calculates the observed value of the index to estimate and mark it on the axis for forming a visualized fuzzy radar evaluation chart. Obviously, this fuzzy evaluation model not only reduces the testing cost but also makes the quality level quickly meet the requirements of the specifications. Further, the radar chart can reduce the risk of misjudgment attributable to sampling errors and help improve the accuracy of evaluation by a confidence-upper-limit-based fuzzy evaluation model. Therefore, this easy-to-use visualized fuzzy radar evaluation chart is used as an evaluation interface, which has good and convenient management performance to identify and improve critical-to-quality quickly. Improving the quality of the process before the product is completed will also have the advantage of reducing social losses and environmental damage costs. [ABSTRACT FROM AUTHOR]

• Measured mineral grades generally confirmed geochemical static test results. • Mineralogy did not explain pH > 7 in humidity cell tests; liberation data were needed. • Mineralogy/texture data enabled sampling error and confidence interval assessment. • Sampling error evaluation for coarse material is key for accurate ARD assessment. • Lack of mineralogy and texture data greatly limits ARD test result interpretation. The value of quantitative mineralogy and texture is often not fully appreciated within minerals applications, and particularly so in the analysis of acid rock drainage (ARD). This is partly due to the absence of a clear understanding as to why quantitative textural tools such as QEMSCAN are valuable for ARD assessment. Additionally, most ARD prediction work is performed on a coarse particle scale, for which statistical representativeness of quantitative textural and mineralogical data becomes difficult to achieve. The current study provides an application of mineralogical and textural data (Fe-sulfide liberation, association, grain size distribution) to geochemical characterisation and humidity cell tests and applies these data to the estimation of the fundamental sampling error (FSE) and mineralogical error through binomial distribution and confidence intervals for liberation data. For the ARD characterisation tests, the mineralogy was key in interpreting the classification of the samples as potentially acid forming, non-acid forming or uncertain. For ARD prediction tests, the large degree of Fe-sulfide encapsulation in intermediate weathering, slow weathering and inert minerals aided in understanding the circumneutral behaviour of potentially acid forming and uncertain samples after 60 weeks of the humidity cell testing. The particle size distribution, in conjunction with texture assessment, showed that ±50% of the Fe-sulfides were unliberated, leading to the expectation that reactivity in the humidity cells would occur predominantly as a result of mineral reaction in finer fractions. The evaluation of uncertainties suggested that "one size fits all" tools such as Gy's safety line or the binominal distribution approximation may not be adequate in all cases, particularly for coarse material, such as that of the parent samples or humidity cell tests. In these situations, material-specific approaches for error consideration should be taken, which in this study were the calculation of the FSE for each sample, and the plotting of size-by-size confidence intervals for the Fe-sulfide liberation data. [ABSTRACT FROM AUTHOR]

The quality characteristics with unilateral specifications include the smaller-the-better (STB) and larger-the-better (LTB) quality characteristics. Roundness, verticality, and concentricity are categorized into the STB quality characteristics, while the wire pull and the ball shear of gold wire bonding are categorized into the LTB quality characteristics. In terms of the tolerance, zero and infinity (∞) can be viewed as the target values in line with the STB and LTB quality characteristics, respectively. However, cost and timeliness considerations, or the restrictions of practical technical capabilities in the industry, mean that the process mean is generally far more than 1.5 standard deviations away from the target value. Researchers have accordingly proposed a process quality index conforming to the STB quality characteristics. In this study, we come up with a process quality index conforming to the LTB quality characteristics. We refer to these two types of indices as the unilateral specification process quality indices. These indices and the process yield have a one-to-one mathematical relationship. Besides, the process quality levels can be completely reflected as well. These indices possess unknown parameters. Therefore, sample data are required for calculation. Nevertheless, interval estimates can lower the misjudgment risk resulting from sampling errors more than point estimates can. In addition, considering cost and timeliness in the industry, samples are generally small, which lowers estimation accuracy. In an attempt to increase the accuracy of estimation as well as overcome the uncertainty of measured data, we first derive the confidence interval for unilateral specification process quality indices, and then propose a fuzzy membership function on the basis of the confidence interval to establish the two-tailed fuzzy testing rules for a single indicator. Lastly, we determine whether the process quality has improved. [ABSTRACT FROM AUTHOR]