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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]

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]

With the rapid development and evolution of the Internet-of-Things (IoT) and big-data analysis technologies, faster and more accurate production data analysis and process capability evaluation models will bring industries closer to the goal of smart manufacturing. Small sample sizes are also common, due to destructive testing, the high costs of detection, and insufficient technological capacity, and these undermine the reliability of the statistical method. Many studies have pointed out that a confidence-interval-based fuzzy decision model can incorporate accumulated data and expert experiences to increase testing accuracy for small samples. Therefore, this study came up with a confidence-interval-based fuzzy decision model based on a process yield index. The index not only reflects process capability but also has a one-to-one mathematical relation with the process yield so that it is convenient to apply in practice. The proposed model not only diminishes the probability of misjudgment resulting from sampling error but also improves the accuracy of testing under the situation of small sample sizes, thereby contributing to the development of smart manufacturing. [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]

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]

In the face of fierce global competition, firms are outsourcing important but nonessential tasks to external professional companies. Corporations are also turning from competitive business models to cooperative strategic partnerships in hopes of swiftly responding to consumer needs and enhancing overall efficiency and industry competitiveness. This research developed an outsourcing partner selection model in hopes of helping firms select better outsourcing partners for long-term collaborations. Process quality and manufacturing time are vital when evaluating outsourcing partner. We therefore used process capability index C p m and manufacturing time performance index I h in the proposed model. Sample data from random samples are needed to calculate the point estimates of indices, however, it is impossible to obtain a sample with a structure completely identical to that of the population, which means that sampling generates unavoidable sampling errors. The reliability of point estimates are also uncertain, which inevitably leads to misjudgment in some cases. Thus, to reduce estimate errors and increase assessment reliability, we calculated the 1 0 0 (1 − α) % confidence intervals of the indices C p m and I h , then constructed the joint confidence region of C p m and I h to develop an outsourcing partner selection model that will help firms select better outsourcing partners for long-term collaborations. We also provide a case as an illustration of how the proposed selection model is implemented. [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]

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]

Evidence is accumulating about the impacts of plastics on marine life. The prevalence of plastics in seabird nests has been used as an indicator of levels of this pollutant in the ocean. However, the lack of a framework for defining sample sizes and errors associated with estimating the prevalence of plastic in nests prevents researchers from optimising time and reducing impacts of fieldwork. We present a method to determine the confidence intervals for the prevalence of debris in seabird nests and provide, for the first time, information on the prevalence of these items in nests of the Hartlaub's gull Larus hartlaubii , the African penguin Spheniscus demersus , the great white pelican Pelecanus onocrotalus , and the white-breasted cormorant Phalacrocorax lucidus in South Africa. The method, based on observations and resampling simulations and tested here for nests of 12 seabird species from 15 locations worldwide, allows for straightforward hypothesis testing. Appropriate sample sizes can be defined by combining this method with a Bayesian approach. We show that precise estimates of prevalence of debris in nests can be obtained by sampling around 250 nests. Smaller sample sizes can be useful for obtaining rough estimates. For the Hartlaub's gull, the African penguin, the great white pelican, and the white-breasted cormorant, debris were present in 0.75%, 3.00%, 6.41%, and 25.62% of the respective nests. Our approach will help researchers to determine errors associated with the prevalence of debris recorded in seabird nests and to optimise time and costs spent collecting data. It can also be applied to estimate confidence intervals and define sample sizes for assessing prevalence of plastic ingestion by any organism. Image 1 • A method to define errors and sample size for the prevalence of debris in nests. • We use data from 12 seabird species from 15 locations worldwide. • Sampling 250 nests provide precise estimates of prevalence of debris. • Our method can be used also for data on prevalence of debris ingestion. • The method is freely available as an R package. A method for defining confidence intervals and sample size for estimating the prevalence of plastic debris in seabird nests. [ABSTRACT FROM AUTHOR]

We explore the Monte Carlo steps required to reduce the sampling error of the estimated 99.9% quantile within an acceptable threshold. Our research is of primary interest to practitioners working in the area of operational risk measurement, where the annual loss distribution cannot be analytically determined in advance. Usually, the frequency and the severity distributions should be adequately combined and elaborated with Monte Carlo methods, in order to estimate the loss distributions and risk measures. Naturally, financial analysts and regulators are interested in mitigating sampling errors, as prescribed in EU Regulation 2018/959. In particular, the sampling error of the 99.9% quantile is of paramount importance, along the lines of EU Regulation 575/2013. The Monte Carlo error for the operational risk measure is here assessed on the basis of the binomial distribution. Our approach is then applied to realistic simulated data, yielding a comparable precision of the estimate with a much lower computational effort, when compared to bootstrap, Monte Carlo repetition, and two other methods based on numerical optimization. [ABSTRACT FROM AUTHOR]