Constructing control charts for autocorrelated data using an exhaustive systematic samples pooled variance estimator

SPC with positive autocorrelation is well known to result in frequent false alarms if the autocorrelation is ignored. The autocorrelation is a nuisance and not a feature that merits modeling and understanding. This paper proposes exhaustive systematic sampling, which is similar to Bayesian thinning except no observations are dropped, to create a pooled variance estimator that can be used in Shewhart control charts with competitive performance. The expected value and variance are derived using quadratic forms that is nonparametric in the sense no distribution or time series model is assumed. Practical guidance for choosing the systematic sampling interval is offered to choose a value large enough to be approximately unbiased and not too big to inflate variance. The proposed control charts are compared to time series residual control charts in a simulation study that validates using the empirical reference distribution control limits to preserve stated in-control false alarm probability and demonstrates similar performance.

众所周知，若忽略自相关效应，带有正自相关的统计过程控制（Statistical Process Control, SPC）常会频繁触发虚警。自相关属于干扰项，而非值得建模与深入研究的特性。本文提出穷尽系统抽样方法——该方法与贝叶斯稀疏化（Bayesian thinning）类似，但无需丢弃观测样本——以构建可应用于休哈特控制图的合并方差估计量，且具备颇具竞争力的性能表现。本文采用二次型推导该估计量的期望与方差，此方法属于非参数范畴，即无需假设任何分布或时间序列模型。本文还给出了选择系统抽样间隔的实用指南，建议选取足够大的间隔以保证估计量近似无偏，同时避免间隔过大导致方差被高估。本文通过仿真研究将所提出的控制图与时间序列残差控制图进行对比：该仿真验证了采用经验参考分布控制限可维持预设的受控状态虚警概率，且证明了两种控制图的性能相近。