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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]

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]

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]