Monitoring attributes is crucial in industrial settings where quality features are not directly measurable. This study introduces a modified Cumulative Sum (CUSUM) scheme, named wCUSUM, to enhance the efficiency of monitoring attribute characteristics.
The wCUSUM scheme improves detection capability by elevating the difference between the actual and in-control numbers of nonconforming items to an exponent w. The charting parameters of the wCUSUM scheme are optimized to minimize the Average Number of Defectives (AND) across out-of-control scenarios while satisfying the constraint of the in-control Average Time to Signal (ATS0). A comparative analysis evaluates the wCUSUM scheme’s performance against the semi-optimal wCUSUM chart proposed by Wu et al. (2008). Sensitivity analysis is conducted to examine the impact of design parameters and inertia on the performance of the wCUSUM chart. A solar panel manufacturing case study demonstrates the proposed chart’s superiority.
The optimal wCUSUM outperforms the semi-optimal wCUSUM1 (w = 1) by 13.21%, wCUSUM1.5 (w = 1.5) by 10.58% and wCUSUM2 (w = 2) by 20.93% in terms of AND under different settings. The wCUSUM enhances detection speed by 19% and 51%, assuming uniform and Rayleigh distributions of the shift, respectively, in comparison to its traditional counterpart. In addition, the wCUSUM outperforms the traditional scheme by 21% in terms of the Expected value of the out-of-control Average Number of Observations to Signal (EANOS). The case study shows a 65% detection efficacy improvement over the semi-optimal wCUSUM.
The proposed wCUSUM chart offers practitioners a robust, economic and efficient tool for monitoring attribute processes. Although its current design aims to monitor a single attribute characteristic, future work could explore its application in multi-attribute scenarios.
This study introduces a novel wCUSUM scheme, tailoring the exponent w to achieve optimal performance. This approach supports customized control chart designs, enhancing adaptability to diverse process monitoring needs.
