Confidence interval-based fuzzy testing approach for Six Sigma Quality Index

Purpose This study aims to enhance estimation accuracy and address uncertainty in measurement data by deriving confidence intervals for the Six Sigma Quality Index based on statistical inference results. A fuzzy testing method is then proposed, utilizing confidence intervals as an evaluation framework for process quality. Design/methodology/approach First, confidence intervals for the Six Sigma Quality Index are derived based on the statistical inference results. Next, these confidence intervals are employed to construct a fuzzy estimation of the index. Finally, fuzzy numbers and their membership functions are developed to create a fuzzy hypothesis testing model using the derived confidence intervals. Findings The fuzzy testing method proposed in this study is grounded in the use of confidence intervals. It not only mitigates the risk of misjudgment caused by sampling errors but also offers a more comprehensive approach compared to traditional statistical testing methods. Originality/value The Six Sigma Quality Index functions not only as a bridge between businesses and customers but also as a tool for internal engineers to assess and analyze processes and propose improvements. However, since the index involves unknown parameters, sampled data are employed for estimation. To improve estimation accuracy and address uncertainty in measurement data, this paper derives the confidence intervals of the Six Sigma Quality Index based on statistical inference results. Building on these results, it proposes a fuzzy testing method that utilizes confidence intervals as a novel approach for evaluating process quality.