Development of an Efficient CUSUM Control Chart for Monitoring the Scale Parameter of the Inverse Maxwell Distribution in Asymmetric, Non-Normal Process Monitoring with Industrial Applications

Control charts are commonly practical as diagnostic tools in statistical applications to recognize probable changes in a process. Control charts find general use as diagnostic tools in statistics in the detection of probable shifts in a process. Among the variety of methods of detection of smaller shifts in processes, the cumulative sum (CUSUM) chart is the most useful in general use. The standard CUSUM chart is often based on the normal distribution, an assumption that does not often align with the quality characters of the majority of real processes. However, many real-world processes exhibit asymmetric and heavy-tailed behavior, which limits the performance of traditional symmetric control chart models. This study presents a new CUSUM control chart based on the inverse Maxwell (IM) distribution and terms it the IMCUSUM chart. The proposed chart’s performance is assessed based on run-length (RL) metrics, which comprise the RL average, the standard deviation of RL, and the median RL. Comparison with the existing IM exponentially weighted moving average (IMEWMA) chart is performed. The results reveal that the proposed IMCUSUM chart performs better compared with the existing IMEWMA chart, especially in the detection of small and moderate shifts in processes. The practical application of the proposed IMCUSUM chart is demonstrated with the application of the proposed and existing control charts in the survival analysis of the lifetimes of brake pads of cars. This real application example highlights the practical application of the proposed IMCUSUM chart in real processes.