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最优的CUSUM控制图与动态非随机控制极限和给定的采样策略,用于小样本的测序序列
Dong Han1, Fugee Tsung2, Lei Qiao3
1Department of Statistics, Shanghai Jiao Tong University, Shanghai, People's Republic of China.
Journal of applied statistics
|March 25, 2024
概括
这项研究引入了对照图的新性能测量方法,发现统一的抽样策略优化了对小样本序列的累积总和 (CUSUM) 图的变化点检测.
科学领域:
- 统计过程控制 统计过程控制
- 质量管理质量管理.
- 变化点检测检测 变化点检测
背景情况:
- 传统的控制图表通常假定样本大小很大,这限制了它们在具有有限或小样本序列的场景中的有效性.
- 评估采样策略对控制图表表现的影响对于准确的过程监控至关重要.
- 累积总和 (CUSUM) 控制图对过程参数中小而持续的变化很敏感.
研究的目的:
- 提出一种新的性能测量方法,用于评估控制图的检测能力,并采用有限或小样本序列的特定采样策略.
- 根据拟议的措施,证明使用动态非随机控制极限和定义的抽样策略的CUSUM控制图的最佳性.
- 用CUSUM图表来比较各种采样策略在变化点检测中的监测性能.
主要方法:
- 开发一种新的性能指标,用于评估在小样本环境中的控制图表检测.
- 根据拟议的绩效衡量标准,建立一个动态CUSUM控制图的最佳性条件的理论证明.
- 数字模拟和对现实世界地震数据的分析,以评估不同的采样策略.
- 对六种不同的采样策略进行比较分析,重点关注它们在变化点检测中的有效性.
主要成果:
- 拟议的性能测量有效地评估了有限样本序列的控制图检测能力.
- 具有动态非随机控制极限和特定采样策略的CUSUM控制图可以实现最佳性能.
- 不同的采样策略显著影响了CUSUM图表在变化点检测中的监测性能.
- 在评估的策略中,统一的抽样策略证明了最有效的监测性能.
结论:
- 拟议的绩效指标为评估有限数据的控制图表提供了一个强大的框架.
- 优化采样策略对于提高CUSUM图表在检测过程变化的灵敏度和准确性至关重要.
- 统一抽样成为使用CUSUM图表在小样本场景中检测变化点的优越策略,提供更好的监测效率.
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