As the environment and information-technology conditions of the Internet of Things matured, various applications were launched. In education, e-learning is promoted so that students’ learning is no longer restricted to the classroom. E-learning schedules are flexible, and learners’ commuting costs are low. Apparently, improving the quality of e-learning systems can enhance learners’ learning effectiveness, satisfaction, engagement, and learning efficacy. A performance evaluation matrix is a useful tool for collecting users’ opinions to assess the performance of an operating system, and it is widely used to evaluate and improve performance in numerous industries and organizations. Therefore, this study used this matrix to construct a model for evaluation and analysis, providing suggestions on improving e-learning systems. This approach maintained the simple response model of Likert scales, which increases the efficiency and accuracy of data collection. Furthermore, the fuzzy membership function of the discriminant index was constructed based on the confidence interval, thereby solving the problems of sampling error and the complexity of collecting fuzzy linguistic data. Besides, we simplified calculations by standardizing test statistics to increase evaluation efficiency. As a result, this study improved the quality of e-learning system, enhanced users’ learning effectiveness, satisfaction, and engagement, and achieved the goal of sustainability.

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 ($\infty$) 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.

After a product has undergone a manufacturing process, it usually has several important quality characteristics. When the process quality of all quality characteristics meets the requirements of the quality level, the process quality of the product can be guaranteed to satisfy customers’ needs. A large number of studies have pointed out that good process quality can raise product yield and product value; at the same time, it can reduce the ratio of rework and scrap, achieve the effect of energy saving and waste reduction, and contribute to the sustainable operation of enterprises as well the environment. Since the six sigma method combines the statistical analysis method of manufacturing cost and production data, it is a useful tool for process improvement and process quality enhancement. Therefore, this paper adopted the six sigma-define, measure, analyze, improve and control (DMAIC) improvement process to lift the manufacturing process quality of multi-characteristic products. Besides, the Taguchi process capability index is one of the commonly used tools for quality assessment in the industry. Not only can it reflect the process loss, but it also can ensure the process yield when the index value is large enough. Consequently, this paper discussed the relationship between the Taguchi process capability index and the six sigma quality level. Meanwhile, the entire six sigma DMAIC improvement process was built on the basis of the process capability index and developed by the method of statistical quality control. Hence, the proposed method is very convenient for process engineers to apply, as well as is helpful for enterprises to move toward the goal of smart manufacturing and sustainability.

Reliability and product process quality are essential in meeting market demand and enhancing competitiveness in the machine tool industry. In addition, manufacturing time performance is also one of the important indices. Therefore, this paper focuses on process quality and manufacturing time and defines a manufacturing time performance index to feedback the acceptance rate of the manufacturing time. The process performance evaluation chart delineated the observations of variations in various workstations, and, hence, in controlling the stability of the work process. The Six Sigma quality indices are constructed by the process accuracy indices and precision indices are represented by X-axis and Y-axis respectively. The process quality evaluation chart evaluates the level of the process quality, as well as proposes the direction of improvement. The manufacturing time performance—Z-axis is used to assess whether the manufacturing time performance meets the requirements. The process performance evaluation chart constructed by this paper makes it easier for researchers to observe which workstations have a process variation in the process, to control the stability of the process effectively, to provide the improvement reference for staff on the scene and to enhance the competitiveness of the industry.

This paper constructs a performance evaluation matrix (PEM) with beta distribution. Beta is between zero and one, making it a suitable indicator to describe customer ratings of importance and satisfaction from 0% to 100%. According to the spirit of ceaseless improvement put forward by total quality management, the average ratings are set as the standard, and then the coordinates of each satisfaction and importance item is located in the performance areas. This makes it easy to identify critical-to-quality items that require improvement. However, the data collection method of questionnaires inevitably involves sampling error, and the opinions of customers are often ambiguous. To solve these problems, we constructed a fuzzy testing method based on confidence intervals. The use of confidence intervals decreases the chance of misjudgment caused by sampling errors, and more precisely gets closer to customers’ voices. This result is more reasonable than the traditional statistical testing principle. The proposed methods are applied to assessment of a computer-assisted language learning (CALL) system to display their competence.

Whether it is important components of a machine tool itself or various important components processed by the machine tool, many vital quality characteristics mostly belong to the smaller-the-better type. When the process quality levels of these quality characteristics do not attain to the criteria, friction loss may increase during the machine operation, affecting not only the process precision and accuracy but also the lifetime of the product. Therefore, this study applied a smaller-the-better six-sigma quality index simultaneously demonstrating process quality level and process yield. Besides, in coping with statistical process control data, a one-tail confidence-interval-based fuzzy testing method was developed to evaluate process quality. Because this approach is built on the basis of confidence intervals, it can reduce the possibility of misjudgment resulting from sampling errors as well as integrate past experience to enhance the accuracy and precision of the assessment, and then it can grasp the timeliness of improvement.