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This study aims to create a performance evaluation model for the food processing machinery industry. The goal is to help food processing plants improve both process quality and competitiveness. Additionally, component failures may disrupt the continuous operation of the food processing machine, potentially resulting in insufficient production and delays in delivery, which in turn leads to cost losses. For the sold food processing machinery, decreases in the average number of failures within a unit of time, the average repair response time when a failure occurs, and the average repair duration are three crucial factors in minimizing the total expected loss due to machine failures. Based on these three important factors, this study established the following evaluation indices: (1) the processing performance index, (2) the repair reporting performance index, and (3) the maintenance performance index. These indices serve as tools for assessing the performance of the three key operational aspects. This study employed a radar chart to construct the evaluation model, which can directly compare the critical values with the point estimates of three indices. Consequently, this approach can judge whether the operational performance has achieved the required level. This can maintain the simplicity and usability of point estimates while reducing the risk of misjudgment due to sampling errors.

Abstract 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.

The rapid progression of emerging technologies like the Internet of Things (IoT) and Big Data analytics for manufacturing has driven innovation across various industries worldwide. Production data are utilized to construct a model for quality evaluation and analysis applicable to components processed by machine tools, ensuring process quality for critical components and final product quality for the machine tools. Machine tool parts often encompass several quality characteristics concurrently, categorized into three types: smaller-the-better, larger-the-better, and nominal-the-better. In this paper, an evaluation index for the nominal-the-better quality characteristic was segmented into two single-sided Six Sigma quality indexes. Furthermore, the process quality of the entire component product was assessed by n single-sided Six Sigma quality indexes. According to numerous studies, machine tool manufacturers conventionally base their decisions on small sample sizes (n), considering timeliness and costs. However, this often leads to inconsistent evaluation results due to significant sampling errors. Therefore, this paper established fuzzy testing rules using the confidence intervals of the q single-sided Six Sigma quality indices, serving as the fuzzy quality evaluation model for components of machine tools.

Foreign language learning courses can be regarded as a service operation system, and a complete foreign language learning course performance evaluation model can help improve the effectiveness of student learning. The performance evaluation matrix (PEM) is an excellent tool for evaluation and resource management decision making, and the administrator uses the satisfaction and the importance indices to establish evaluation coordinate points based on the rules of statistical testing. The coordinate points of all service items are plotted into the PEM to grasp the full picture and to make decisions on what to improve or to consider resource transfers so as to elevate the overall satisfaction of the entire service. However, plotting all the coordinate points on the PEM can only be performed by programming, which will lead to limitations in practice. Therefore, instead of the above evaluation rules, this article uses the confidence intervals of decision-making indicators to form a validity evaluation table, to decide which teaching service items should be improved, maintained, or transferred to improve the satisfaction of the entire service system. This form of performance evaluation can be completed using any commonly used word-processing software, so it is easy to apply and promote. Finally, this article provides an applied example to illustrate the proposed method.

Global warming has led to the continuous deterioration of the living environment, in which air quality directly affects human health. In addition, the severity of the COVID-19 pandemic has further increased the attention to indoor air quality. Indoor clean air quality is not only related to human health but also related to the quality of the manufacturing environment of clean rooms for numerous high-tech processes, such as semiconductors and packaging. This paper proposes a comprehensive model for evaluating, analyzing, and improving the operational performance of air cleaning equipment. Firstly, three operational performance evaluation indexes, such as the number of dust particles, the number of colonies, and microorganisms, were established. Secondly, the 100(1− α)% upper confidence limits of these three operational performance evaluation indexes were deduced to construct a fuzzy testing model. Meanwhile, the accumulated value of ϕ was used to derive the evaluation decision-making value. The proposed model can help companies identify the key quality characteristics that need to be improved. Furthermore, the competitiveness of cooperative enterprises towards smart manufacturing can be strengthened, so that enterprises can not only fulfill their social responsibilities while developing the economy but also take into account the sustainable development of enterprises and the environment.

A variety of process capability indices are applied to the quantitative measurement of the potential and performance of processes in manufacturing. As it is easy to understand the formulae of these indices, this method is easy to apply. Furthermore, a process capability index is frequently utilized by a manufacturer to gauge the quality of a process. This index can be utilized by not only an internal process engineer to assess the quality of the process but also as a communication tool for an external sales department. When the manufacturing process deviates from the target value T, the process capability index CPMK can be quickly detected, which is conducive to the promotion of smart manufacturing. Therefore, this study applied the index CPMK as an evaluation tool for process quality. As noted by some studies, process capability indices have unknown parameters and therefore must be estimated from sample data. Additionally, numerous studies have addressed that it is essential for companies to establish a rapid response mechanism, as they wish to make decisions quickly when using a small sample size. Considering the small sample size, this study proposed a 100 (1 − α)% confidence interval for the process capability index CPMK based on suggestions from previous studies. Subsequently, this study built a fuzzy testing model on the 100 (1 − α)% confidence interval for the process capability index CPMK. This fuzzy testing model can help enterprises make decisions rapidly with a small sample size, meeting their expectation of having a rapid response mechanism.

As global warming becomes increasingly serious, humans start to consider how to coexist with the natural environment. People become more and more aware of environmental protection and sustainable development. Therefore, in the pursuit of economic growth, it has become a consensus that enterprises should be responsible for the social and ecological environment. Regarding the manufacturing of electronic devices, as long as both component production quality and assembly quality are ensured, consumers can be provided with high-quality, safe, and efficient products. In light of this trend, enhancing product availability and reliability can reduce costs and carbon emissions resulting from repairing or replacing components, thus becoming a vital factor for corporate and environmental sustainability. Accordingly, enterprises enhance their economic benefits as well as have the effects of energy conservation and waste reduction by extending products’ service lifetime and increasing their added value. According to several studies, it takes a long time to retrieve electronic products’ lifetime data. Moreover, acquiring complete samples is often challenging. Consequently, when analyzing real cases, samples are usually collected using censoring techniques. The type-I right censoring data is suitable for industrial processes. Thus, this study utilized type-I right censoring sample data to estimate the lifetime performance index. It usually takes a large amount of time to access lifetime data for electronic products and it is often impossible to obtain complete samples since the size of the sample is usually small. Hence, to avoid misjudgment caused by sampling errors, this study followed suggestions from existing research and applied fuzzy tests built on confidence intervals to establish a fuzzy evaluation model for the lifetime performance index. This model helps relevant electronic industries not only evaluate the lifetime of their electronic components but also instantly seize opportunities for improvement.

Some studies have shown that any part machined by an outsourcer usually has several basic quality characteristics. When the outsourcer’s process capabilities are insufficient, the defective rate of various quality characteristics of the product will increase, thereby raising the rework rate and scrap rate. As a result, maintenance costs will go up, economic value will decrease, and even carbon emissions can increase during the production process. In addition, the process capability index and the radar chart are widely used in engineering management and other fields. Since process indicators often contain unknown parameters, sample data are needed for evaluation. With the rapid development of the Internet of Things and big data analysis, many companies regard rapid response as a basic requirement for timeliness and cost consideration. Therefore, companies often have to evaluate the process quality of ten small samples and decide whether to make some improvements. In order to solve the above problems, this study proposed a fuzzy radar chart evaluation model for the process quality of multi-quality characteristic parts based on the process capability index. Using this model can help all parts manufacturers continue to improve the quality of their machined parts as well as reduce their rework and scrap rates. Meanwhile, carbon emissions can be lessened during the production process, and companies can fulfill their social responsibilities. This fuzzy radar chart evaluation model is based on confidence intervals. As the company’s past experience is incorporated, the evaluation accuracy can be maintained even with a smaller sample size. Furthermore, the fuzzy radar evaluation chart can simultaneously evaluate the process capabilities of all quality characteristics of the part. In addition to making it easier for manufacturers to master all quality characteristics, quality process capability can also help them seize improvement opportunities.

In facing the many negative impacts of global warming on the earth’s environment, the machining industry must reduce the rates of product rework and scrap in the manufacturing process by enhancing the process quality of the processed product. According to the concept of the Taguchi loss function, the closer the measured value of the processed product is to the target value T, then the longer the mean time between failures (MTBF) of the product. Clearly, raising the process quality of the processed product can effect energy saving and waste reduction during production and sales, which can help enterprises fulfill their corporate social responsibilities. On the basis of the Taguchi loss function, this study used the process expected loss to evaluate the process loss. Next, the process expected loss was used as an evaluation index, in which the accuracy index and the precision index can help the machining industry find the direction for improvement. Additionally, this study first derived a confidence interval of the process expected loss. Then, it was built on the confidence interval, and a confidence interval-based fuzzy test was developed for the process expected loss. Finally, an empirical example was adopted to explain the application of the fuzzy evaluation model of the machining process proposed in this paper.

Process Capability Indices (PCIs) are devices widely used in the industry to evaluate process quality. The commonly used process capability indices all contain accuracy indices and precision indices. As the accuracy index is closer to zero, the process accuracy is higher. The precision index mainly represents the extent of process variation. As the value is smaller, the process variation is smaller, that is, the precision is higher. In fact, process capability indices are the functions of accuracy indices and precision indices. Obviously, as long as accuracy indices and precision indices are controlled, the process capability indices can be controlled as well. Therefore, this study first derived accuracy and precision control charts to observe not only process accuracy but also process precision. Then, this study adopted in-control data to acquire a 100 (1 − α)% confidence region of an accuracy index and a precision index, with which statistical tests were performed. Subsequently, according to the definition of the six sigma quality level, both indices were examined. Furthermore, based on the testing results, suggestions for process improvement were proposed, including correcting the direction of process deviation and deciding whether to reduce process variation. Finally, this study demonstrated the applicability of the proposed model using an empirical example.

The improvement process of six-sigma DMAIC refers to the process that the industry performs to enhance process quality via the following five procedures: (1) define, (2) measure, (3) analyze, (4) improve, and (5) control. It is a common tool used in the industry to ameliorate and enhance process quality. In addition, the process capability index is a tool that the industry most frequently uses to measure process quality. Though many studies have discussed six-sigma methods, none of the specific theoretical models could be provided as a reference for the above five DMAIC improvement steps, making it difficult to control the effect. In order to solve this problem, this paper developed the multi-characteristic process capability analysis chart, MPCAC, using the process capability index and applied the method of statistical inference as a tool promoting define, measure, and analyze in the improvement process of six-sigma DMAIC. Additionally, the testing of the orthogonal table in the Taguchi method can efficiently assist process engineers in finding the optimum combination of machining parameters to improve or boost the process quality level of the quality characteristics by reducing the number and the cost of experiments. Therefore, this paper then adopted the testing of the orthogonal table in the Taguchi method as a tool for process improvement in the fourth step. Finally, according to the optimal combination of machining parameters improved in the fourth step, a standard operating procedure for transistor gaskets was established as a tool for process control in the fifth step.

This study proposes the Spa-product capability analysis chart (Spa-PCAC), which can widely represent multiple process capabilities with asymmetric tolerances of Smaller-the-Better, Larger-the-Better, and Nominal-the-Best characteristics. Process capability index Spa is generated based on index Spk, which uses asymmetric tolerances to reasonably measure process capabilities. The interval estimates of the indices are derived to reliably assess process capabilities. The Six-Sigma-based quality-level and its connection with the process yield are introduced in the capability zone of Spa-PCAC to check if the process capabilities can meet the requirements. One example of an entire product is given for application.

Taiwan is a world-leader in wafer foundry services and IC packaging and testing. Wire bonding is a crucial process in the overall IC-packaging industry chain. Thus, this paper proposes a process-quality evaluation model for wire bonding with multiple gold wires. We chose process quality indices as a tool of evaluation fully mirroring process yield and quality levels. These indices contain unknown parameters and thus require sample data to estimate. We first derived the uniformly minimum variance unbiased estimator of the indices and calculated the upper confidence limits of the indices based on DeMorgan's theorem and Boole's inequality. The upper confidence limits of the indices were then employed to create a confidence interval-based fuzzy membership function, in order to improve the accuracy of estimation as well as solve the problem of uncertainty of the measured data. Next, we obtained the fuzzy critical value and used index estimates and the fuzzy critical value to establish fuzzy test rules. Next, we marked the fuzzy critical value on the axes of a radar chart, which is a visualization evaluation tool, and connected neighboring critical points to create a critical region in the form of a regular polygon. The observed values of the indices were then marked on the axes to produce a visualized fuzzy radar evaluation chart. This fuzzy radar evaluation chart has a solid foundation in statistical inference, and evaluation rules were established using precise fuzzy test methods. Not only is this fuzzy radar evaluation chart easy to use, but it also reduces the chance of misinterpretations made by sampling errors, so that the accuracy of evaluation can be enhanced.

With the gradual maturity and popularization of the Internet of Things (IoT), technologies of measurement and analysis for production data have also been continuously advanced, realizing the collection of large production data [...]

When the lifetime of an electronic component does not reach the required level, it can be enhanced by means of the paralleling current sharing backup system or the redundant backup system. The lifetime of the redundant backup system is the sum of lifetimes of all electronic components, which is the maximum of all the electronic components’ lifetimes, compared with the lifetime of the parallel current sharing backup system. For the purpose of enhancing products’ reliability, electronic goods are usually designed with spare electronic components. If it is assumed that there are m−1 redundant backup components for each electronic product, then the lifetime of the electronic product will be distributed as a Gamma distribution with two parameters—m and λ, where λ is the mean for each lifetime of each electronic component. According to numerous studies, the sample size is not large, as it takes a long time to test the lifetime of an electronic product, and enterprises consider cost and timeliness. This paper concerns the performance index of the lifetime of the electronic product. Therefore, based on the confidence interval, this paper aims to develop a fuzzy testing model. As this model can integrate past data and expert experience, the testing accuracy can be retained despite small-sized samples. In fact, through adopting the testing model proposed by this paper, companies can make precise and intelligent decisions instantly with the use of small-sized samples to grasp the opportunities for improvement.

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.

Many studies have pointed out that the-smaller-the-better quality characteristics (QC) can be found in many important components of machine tools, such as roundness, verticality, and surface roughness of axes, bearings, and gears. This paper applied a process quality index that is capable of measuring the level of process quality. Meanwhile, a model of fuzzy quality evaluation was developed by the process quality index as having a one-to-one mathematical relationship with the process yield. In addition to assessing the level of process quality, the model can also be employed as a basis for determining whether to improve the process quality at the same time. This model can cope with the problem of small sample sizes arising from the need for enterprises’ quick response, which means that the accuracy of the evaluation can still be maintained in the case of small sample sizes. Moreover, this fuzzy quality evaluation model is built on the confidence interval, enabling a decline in the probability of misjudgment incurred by sampling errors.

In order to take into account cost and timeliness and enhance accuracy testing, this study developed the fuzzy number and membership function, using the confidence interval of ratio operating performance index. Subsequently, according to the statistical test rules and the application of the fuzzy number and membership function, a fuzzy evaluation decision model for the operating performance index is proposed, to evaluate if the business performance reaches the needed level. Based on the abovementioned, the evaluation model in this study took into account not only timeliness but also accuracy, so that it could grasp the opportunity of improvement for operating organizations with poor operating performance after being evaluated. This fuzzy evaluation decision model for the operating performance index constructs a fuzzy membership function retrieved from an index’s confidence interval, reducing the chance of miscalculation due to sampling mistakes and improving the efficiency of evaluation. Finally, in order to facilitate the application of readers and the industry, this paper uses cases to explain the proposed fuzzy verification method. On the whole, the model proposed in this paper is a data-based auxiliary tool for the service operating performance improvement strategy.

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.

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.

Many important parts of tool machines all have the important smaller-the-better (STB) quality characteristics. The important STB quality characteristics will impact on the quality of the end-product. At the same time, supplier quality influences the quality and functionality of the end-product, so suppliers must be selected with caution. The six sigma quality index for the STB quality characteristics can directly reflect process quality levels. Besides, this index possesses a mathematical relationship with process yield. Nevertheless, the point estimation will cause the risk of misjudgment, due to sampling errors. As a result, this study applies the confidence interval of the index to a two-tailed fuzzy testing method, in order to select appropriate suppliers. Now that this method is on the basis of the confidence interval, the possibility of misjudgment caused by sampling errors will be reduced, while the precision of the selection will be enhanced. The method can help companies increase product quality, as well as the competitiveness of the industry chain as a whole. Finally, a numerical example is presented to show how to approach this method and its efficacy.

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.

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.

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.

A performance evaluation matrix is based on questionnaires collected from users or customers to pinpoint the performance of a system operation and furthermore to locate the items that need to be improved to upgrade the performance of system operations. To achieve this, this article proposes a discrimination index and applies statistics inference to deduce confidence intervals of the discrimination index. Meanwhile, we refer to Buckley's fuzzy testing method to construct a fuzzy affiliation function and address a fuzzy evaluation criterion for exploring the items considered critical to quality to overcome the complicated problems of the questionnaires' sampling error and interviewees' fuzzy linguistics. The advantages of the method in this article are that it keeps the simple filling pattern of Likert's scale and provides efficacy of data collection. Subsequently, we reduce the fuzzy linguistics and questionnaires' sampling error by statistics inference and fuzzy hypothesis testing. Finally, we use a case study with the computer-assisted language learning system to demonstrate an application of the proposed method. [ABSTRACT FROM AUTHOR]