ABSTRACT

This article not only shows that the CUSUM multi-chart which consists of several CUSUM charts, has the asymptotic optimal performance in jointly detecting and diagnosing the unknown change in a sequence of $i.i.d.$ observations but also provides a design method of optimizing the CUSUM and EWMA multi-charts. The numerical comparisons illustrate that the optimized CUSUM multi-chart has better performance in jointly detecting and diagnosing the mean and variance shifts in $i.i.d.$ normal observations than that of the optimized EWMA multi-chart. A real example for engineering surveillance using the electric power generation data was used to demonstrate the practicality of the schemes.

摘要

本文不仅展示了由多个 CUSUM 图组成的 CUSUM 多图，在联合检测和诊断序列中的未知变化方面具有渐近最优性能。 $\mathrm{一世}.\mathrm{一世}.d.$观察还提供了一种优化 CUSUM 和 EWMA 多图的设计方法。数值比较表明，优化后的 CUSUM 多图在联合检测和诊断均值和方差偏移方面具有更好的性能。$\mathrm{一世}.\mathrm{一世}.d.$正常观测值比优化 EWMA 多图的观测值。使用发电数据进行工程监控的真实示例被用来证明方案的实用性。