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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]

As the Internet-of-Things matures, technologies for the measurement and collection of production data are also improving. What is needed next is an effective information analysis model to aid in the timely adjustment of manufacturing parameters to optimize production. Production data analysis models must be continuously and properly utilized to monitor and maintain process quality. Improving product quality helps to lengthen service life, decrease scrap and rework, and reduce the social losses caused by malfunctions and maintenance. The Taguchi capability index Cpm can fully reflect the losses and yield of processes and is a convenient and effective tool to evaluate and analyze process data in the industry. As it contains unknown parameters, we derived the upper confidence limit (UCL) of Cpm based on collected production data. Due to the fuzzy uncertainties that are common in measurement data, we then used the UCL of the index to construct a fuzzy membership function and propose a fuzzy testing decision-making model to determine whether processes are in need of improvement. Before the proposed fuzzy test methods became full-fledged, we used the concept of sample size and the rules of statistical testing to explain the motivation underlying those methods. In fact, the sample size influences the risk of misjudgment in UCL, and in practice, sample sizes are rarely large due to cost and time considerations, thereby they produce larger UCL with a corresponding decrease in accuracy and increase in risk of misjudgment. The fuzzy test methods proposed in this study are based on statistical inference, and judgement is aided by expertise, thus are capable of solving the problems associated with larger UCL. Therefore, the theoretical foundation of this fuzzy testing decision-making model is the UCL, it can lower the chance of misjudgment caused by sampling errors and increase evaluation accuracy. [ABSTRACT FROM AUTHOR]