Enhanced Process Monitoring for the Maxwell Process via the CUSUM Control Chart and Its Application to the Carbon Fiber Industry

Control charts are the diagnostic tools used in statistical applications for detecting possible changes in a process. One of the effective approaches for identifying smaller shifts in the process under the memory control charts is the cumulative sum (CUSUM) chart. The ordinary CUSUM schemes are designed exclusively on the basis of the normality assumption, which may not hold true for many process quality characteristics in practical scenarios. To address this, the $V_{SQ}$ -chart is frequently utilized for analyzing nonnormal data, with the purpose of detecting sudden changes in the scale parameter of the Maxwell process. However, the $V_{SQ}$ -chart lacks sensitivity to smaller parameter changes. In this work, a novel extension of the $V_{SQ}$ -chart called the Maxwell CUSUM (MXCUSUM) chart is designed to monitor small changes in a process that follows the Maxwell distribution. The MXCUSUM chart exhibits strong detection capabilities across a variety of smaller shift sizes. Through Monte Carlo simulations, the run length properties of the proposed chart are assessed and compared with those of other existing charts. The comparative analysis reveals that the MXCUSUM is more effective at detecting a range of small shift sizes than its existing counterpart is. Finally, two real-life examples are utilized to illustrate the design and implementation procedure of the proposed chart.