Comparing the performance of Max-Mchart, Max-Half-Mchart, and kernel-based Max-Mchart for individual observation in monitoring cement quality

Control charts are one of the tools commonly used to monitor quality. There are three types of control charts, namely the Shewhart, cumulative sum (CUSUM), and exponentially weighted moving average (EWMA). The Shewhart-type control chart is formed with a normal distribution assumption for the data. However, when applied in real cases, especially in cement quality, it is often found that data for quality monitoring does not follow the normal distribution assumption. The cement quality characteristics monitored are blaine, residue, and free lime. When the data is not normally distributed or unknown distribution, it is necessary to monitor quality using control charts with a non-parametric approach. One of the non-parametric methods that can be used for a control chart is the kernel. Kernel is used to obtain a density that corresponds to the data conditions. Simultaneous control charts are more effective in monitoring quality than conventional control charts. The simultaneous multivariate control chart Max-Mchart and Max-Half-Mchart can detect small and large shifts in mean process and variability process. Thus, the proposed chart is called the Kernel-Based Max-Mchart and Kernel-Based Max-Half-Mchart, whose control limit is calculated using the non-parametric bootstrap approach. The Kernel-Based Max-Mchart and Kernel-Based Max-Half-Mchart are more sensitive than the conventional Max-Mchart and Max-Half-Mchart for individual observations in monitoring cement quality. Kernel-Based Max-Mchart and Kernel-Based Max-Half-Mchart outperform the conventional Max-Mchart and Max-Half-Mchart for non-normal data distribution.