Design of attribute control charts under uncertainty with normality analyses: Impact of operator hesitancy during inspection processes in manufacturing industry with a real case application

Control charts (CCs) are one of the most effective tools for tracking variations and stability over time and are widely used generally in manufacturing to monitor and control process’ performance. When using attribute control charts (ACCs), one of the most crucial challenges is addressing uncertainty arising from both the use of linguistic terms (LTs) for quality assessment and inspectors' hesitancy in their judgments. Additionally, analyzing data normality is critical, as CCs are constructed based on the assumption of normally distributed data. To systematically address these uncertainties, our proposed method integrates fuzzy Z-numbers to enhance the robustness of LT evaluations and account for inspector hesitancies in the number of non-conformities per unit with a constant sample size ( u) and number of non-conformities per unit with varying sample sizes (c) ACCs. Additionally, it provides a rigorous framework for assessing data normality under uncertain conditions to ensure the reliability of control limits. Furthermore, a fuzzy Mamdani inference system is integrated into the proposed approach to enhance decision-making accuracy, as it reduces loss of information by providing more sensitive and detailed outputs. These detailed outputs provide valuable support for both managers and operators, enabling more precise decision-making. The proposed approach is validated through on a real-case application in the automotive sector, and its effectiveness is confirmed by average run length (ARL) tests. Additionally, a comparison analysis for the proposed method with some existing methods is summarized. Results obtained indicate that the proposed approach significantly enhances performance by addressing operator hesitancy during inspections and mitigating the imprecision introduced by LTs through computing with words concept.