Control charts are widely used in industrial environments for the simultaneous or separate monitoring of the process mean and process variability. The Max-Mchart is a multivariate Shewhart-type simultaneous control chart that is used when monitoring subgroups. While this sampling design allows the computation of the generalized variance (GV) used to calculate the process variability, a GV chart cannot be plotted for individual observations. Hence, we cannot compute the single statistic in the Max-Mchart. This study aims to overcome the aforementioned issue. To this end, first, we develop a new Max-Mchart for individual observations by utilizing the statistic in the dispersion control chart. Second, instead of the standard normal distribution, we propose a new transformation using a half-normal distribution to calculate the statistic for the process mean and process variability. Thus, the proposed chart is called the Max-Half-Mchart, whose control limit is calculated using the bootstrap approach. An evaluation based on the average run length values shows the robustness of the Max-Half-Mchart for the simultaneous monitoring of the process mean and process variability. The single statistic in the Max-Half-Mchart is more consistent with the statistic in Hotelling's 2 and the dispersion chart than that of the Max-Mchart.
Control charts are extensively used to monitor the production process. When there is more than one variable process are considered, the multivariate control charts are typically employed to monitor the mean vector and the variability process separately. In recent years, control charts have been developed for monitoring mean process and variability process simultaneously in a chart. A Maximum multivariate control chart (Max-Mchart) is one of the simultaneous multivariate control charts relying on exact distribution control limit. The objective of this paper is to evolve Max-Mchart based on Bootstrap control limits. This paper also compares Max-Mchart over the Hotelling T2 and Generalized Variance (GV) control chart. The interpretive examples are implemented to demonstrate the applications of the ZA fertilizer production dataset in carbonation step.
The main purpose of time series analysis is to obtain the forecasting result from an observation for future values. Quantile Regression Neural Network is a statistical method that can model data with non-homogeneous variance with artificial neural network approach that can capture nonlinear patterns in the data. Real data that allegedly have such characteristics is Consumer Price Index (CPI). CPI forecasting is important to assess price changes associated with cost of living as well as identifying periods of inflation or deflation. The purpose of this research is to compare several method of forecasting CPI in Indonesia. The data used in this study during January 2007 until April 2018 period. QRNN method will be compared with Neural Network with RMSE evaluation criteria. The result is QRNN is the best method for forecasting CPI with RMSE 0.95.
A Simultaneous control chart is a well-known tool for monitoring the process mean and process variability with a single chart. In recent decades, many researchers have been interested in developing simultaneous control charts. The Shewhart chart is the most common and simple simultaneous control chart. The Multivariate Maximum control chart (Max-Mchart) is a type Shewhart chart that simultaneously monitors the process of multivariate data. This paper proposes a new transformation using a half-normal distribution to improve the Max-chart performance for subgroup observations. The new proposed chart is called Max-Half-Mchart. The Average Run Length (ARL) results show that the proposed Max-Half-Mchart outperforms the Max-Mchart. Additionally, in real data scenarios, the proposed Max-Half-Mchart is consistent with the statistic in the Hotelling T 2 chart and the Generalized Variance (GV) chart.
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