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.

The method of six-sigma and the index of process capability are both commonly used tools in the industrial community. Process engineers can follow five improvement steps of the six-sigma method, including “define”, “measure”, “analyze”, “improve”, and “control” (DMAIC), aiming to improve and enhance the process quality. However, none of these five improvement steps have a clear corresponding approach. This paper considered process capability indices not only a process quality evaluation tool widely used in the industrial community but also a process quality evaluation and analysis tool adopted by internal engineers. Therefore, this paper applied the method integrating process capability indices and statistical testing to develop execution models for the five improvement steps, DMAIC, of the six-sigma method. First, this paper, based on the concept of yield, not only deduced the relationship between the required value of the process capability index for the product and the process capability index value of the individual quality characteristic but also discussed the definition of the quality level of six-sigma as well as its relationship with the process capability index. Next, according to these results, five improvement execution models of the six-sigma method were developed and served as a reference for the process engineers in the industry to promote the performance of the six-sigma project. The proposed method in this paper applied various normal processes and combined the six-sigma method and process capability indices, both of which are tools commonly used in the industrial community. It also has taken into account the advantages of theoretical contribution and industrial acceptance.