<p>The Six Sigma quality index simultaneously reflects process yield, process capability, and Six Sigma quality standards. It is an effective communication tool between industry professionals and customers. An estimator with small bias and variance can enhance the accuracy of an estimate. Furthermore, many industries often face challenges in decision-making due to timeliness and cost considerations, leading to large confidence intervals from small sample sizes. This results in significant sampling errors and inconsistent evaluation outcomes. To address these issues and improve assessment accuracy, this article proposes a Six Sigma quality index estimator with small bias and variance. Based on this, a confidence-interval-based fuzzy test is also introduced. The proposed model relies on confidence intervals and utilizes a smaller bias estimator to mitigate the chances of misjudgments resulting from sampling errors. Meanwhile, this approach is also beneficial to the advancement of smart manufacturing practices, thereby boosting process quality and product value in the industry.</p>