Optimal Design of an Attribute Control Chart for Monitoring the Mean of Auto‐Correlated and Fine‐Quality Manufacturing Processes by Group Inspection

ABSTRACT

Numerous attribute control charts have been developed to monitor process means; however, most rely on the assumption of statistical independence, rendering them inadequate for modern industrial environments where process variables exhibit significant autocorrelation. This study proposes a novel attribute control chart specifically designed for autocorrelated processes by modeling observations as a first‐order autoregressive [AR(1)] process. By integrating a Cumulative Count of Conforming (CCC) scheme, the proposed chart achieves precise monitoring of the Average Run Length (ARL). The chart's architecture is refined through a rigorous optimization model. To evaluate performance, we provide a comparative analysis assessing the impact of autocorrelation on monitoring effectiveness. Furthermore, a practical manufacturing case study demonstrates the chart's application. This proposed framework facilitates the prompt and accurate surveillance of high‐quality processes, addressing the inherent serial correlation often found in contemporary manufacturing systems.