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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]

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]

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]