This work investigates a two-way communication retrial queue with synchronous working vacation and a constant retrial policy. During the idle time, a server makes an outgoing call after a random length. The service time of the incoming call and outgoing call obeys exponential distribution with different rates. If the incoming call finds all servers to be unavailable, it may or may not enter orbit. All servers immediately go on vacation simultaneously as soon as they find an empty system after the service finishes. During vacation, the servers can provide a service to those incoming calls, but this is at a lower-speed rate. The stationary probability distribution and the ergodic condition are obtained utilizing the matrix geometric technique. Some system characteristics are developed. Using MATLAB software, the variation in average orbit length, idle ratio, and the average number of servers in different server states is plotted for different values of the incoming/outgoing call rate and retrial rate. We further propose a multi-objective optimization model from which the optimal rate of outgoing calls and optimal vacation rate are explicitly obtained.

The semiconductor industry is a rapidly growing sector. As collection technologies for production data continue to improve and the Internet of Things matures, production data analysis improves, thus accelerating progress towards smart manufacturing. This not only enhances the process quality, but also increases product lifetime and reliability. Under the assumption of exponential distribution, the ratio of lifetime and warranty has been proposed as a lifetime performance index for electronic products. As unknown parameters of the index, to use point estimates to assess lifetime performance may cause misjudgment due to sampling errors. In addition, cost and time limitations often lead to small sample sizes that can affect the results of the analysis. Type-II censored data are widely applied in production and manufacturing engineering. Thus, this paper proposes an unbiased and consistent estimator of lifetime performance based on type-II censored data. The 100(1 − α)% confidence interval of the proposed index is derived based on its probability density function. Overly small sample sizes not only make the length estimates of lifetime performance index intervals for electronic products too long, but they also increase sampling errors, which distort the estimation and test results. We therefore used the aforementioned interval to construct a fuzzy test model for the assessment of product lifetime and further help manufacturers to be more prudent and precise to evaluate the performance of product life cycles. A numerical example illustrates the applicability of the proposed model.

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.

The measurement of the process capability is a key part of quantitative quality control, and process capability indices are statistical measures of the process capability. Six Sigma level represents the maximum achievable process capability, and many enterprises have implemented Six Sigma improvement strategies. In recent years, many studies have investigated Six Sigma quality indices, including $Q_{pk}$. However, $Q_{pk}$ contains two unknown parameters, namely $\delta$ and $\gamma$, which are difficult to use in process control. Therefore, whether a process quality reaches the k sigma level must be statistically inferred. Moreover, the statistical method of sampling distribution is challenging for the upper confidence limits of $Q_{pk}$. We address these two difficulties in the present study and propose a methodology to solve them. Boole’s inequality, Demorgan’s theorem, and linear programming were integrated to derive the confidence intervals of $Q_{pk}$, and then the upper confidence limits were used to perform hypothesis testing. This study involved a case study of the semiconductor assembly process in order to verify the feasibility of the proposed method.

The investigation examines English proficiency levels across Taiwanese primary education, revealing a significant divergence in skills characterized by an M-shaped distribution among students in the fifth and sixth grades. To address this disparity, the study employs a performance evaluation method that combines importance–performance analysis (IPA) and the refined Kano model, aiming to identify and improve upon the current deficiencies in English language teaching. Further analytical depth is provided by applying a three-factor theory, which re-evaluates the traditional five-factor framework of the Kano model, informed by a survey of 443 respondents. The analysis identified that, out of twenty evaluative items, four are critical and demand targeted enhancement efforts. The paper has identified four items for enhancement to improve English language instruction quality. Specifically, it suggests that two items from the importance–performance analysis are critically under resourced and require immediate intervention. Additionally, the paper recognizes two items from the Kano model that also need focused improvement. The study recommends swift and targeted actions to address these areas, with the goal of raising the overall standard of teaching. Based on these findings, the study proposes a set of practical recommendations aimed at increasing the overall effectiveness of teaching and fostering an environment that enhances student motivation. The ultimate goal of this study is to support English teachers in primary schools by providing strategic insights that can lead to the enhancement of teaching practices and the amelioration of English language education deficiencies.