Design and Application of a High-Dimensional Robust Control Chart for Joint Monitoring of Location and Scale Parameters

Abstract

In industrial production, statistical process control is a common method used to ensure process stability and product quality. With the development of production technology and the increasing complexity of products, the number of product index parameters that need to be monitored is also increasing, and the traditional control chart method often faces challenges in processing high-dimensional data. For example, the traditional control chart method is applied based on the assumption that the process data distribution is known, and the continuous data is usually assumed to be normally distributed, while many data in the actual process do not follow the normal distribution. Secondly, high-dimensional data often contains complex features, and there are often correlations between variables, which makes it difficult to describe the joint distribution of high-dimensional data. These problems will greatly affect the monitoring effect of the control chart. In view of the above problems and the characteristics of high-dimensional data, this paper first combines the score test statistics with the exponential weighted moving average (EWMA) method after mathematical transformation, and proposes a local statistic to monitor each one-dimensional data stream. Then the correlation between data streams is represented by the appropriate combination of marginal distribution functions, and the global statistics for monitoring high-dimensional data streams are constructed. The control chart proposed in this paper is different from the traditional control chart, it does not need to know the distribution of the process, and can monitor the position parameters and scale parameters simultaneously. The effectiveness and robustness of the control chart are verified by numerical simulation and example analysis.