ABSTRACT

This article considers the problem of jointly monitoring the mean and variance of a process by multi-chart schemes. Multi-chart is a combination of several single charts which detects changes in a process quickly. Asymptotic analyses and simulation studies show that the optimized CUSUM multi-chart has optimal performance than optimized EWMA multi-chart in jointly detecting mean and variance shifts in an $i.i.d.$ normal observation. A real example that monitors the changes in IBM's stock returns (mean) and risks (variance) is used to demonstrate the performance of the above two multi-charts. The proposed method has been compared to a benchmark and it performed better.

摘要

本文考虑了通过多图表方案共同监视过程的均值和方差的问题。多图表是几个单个图表的组合，可快速检测过程中的变化。渐近分析和仿真研究表明，优化的CUSUM多图在联合检测平均和方差变化方面比优化的EWMA多图具有最佳性能。$\mathrm{一世}。\mathrm{一世}。d。$正常观察。监视IBM股票收益（均值）和风险（方差）变化的真实示例用于演示上述两个多重图表的性能。所提出的方法已与基准进行比较，并且性能更好。