运筹与管理2024，Vol.33Issue(3)：82-88,7.DOI:10.12005/orms.2024.0082
非参数自适应EWMA SR控制图及其变采样间隔设计
Design of the Nonparametric Adaptive EWMA SR Control Chart with Variable Sampling Intervals
摘要
Abstract
Traditional control charts like the Shewhart control chart only utilize the current sample information,while the exponentially weighted moving average(EWMA)control chart combines current and historical data through a smoothing constant for improved shift detection ability.However,the performance of these parametric control charts relies heavily on the assumption that the process data follows a specific probability distribution,typically the normal distribution.When this parametric assumption is violated,the control charts can suffer from low detection power and frequent false alarms.This paper will introduce a new nonparametric adaptive exponen-tially weighted moving average(AEWMA)control chart based on the Wilcoxon signed-rank(SR)statistic to monitor process median shifts when the underlying data distribution is unknown or non-normal.The proposed AEWMA SR control chart leverages the robust properties of nonparametric statistics while inheriting the overall superior shift detection capabilities of adaptive schemes.The smoothing constant of the proposed adaptive expo-nentially weighted updating schemeis adjustable based on the magnitude of the monitoring statistic through a discrete error transmission function.This allows the AEWMA SR control chart to automatically emphasize recent or past observations to optimally detect different levels of shifts.To further enhance its detection rapidity,the authors study the properties of the AEWMA SR control chart under a variable sampling interval(VSI)strategy.Two sampling intervals are utilized:a shorter interval when the statistic falls in a warning zone around the center line to quickly detect any potential shifts,and a longer interval in the safety zone to reduce sampling costs.The exact run-length performance measures including the average run length(ARL)and the average time to signal(ATS)are derived using the Markov chain approach.An optimization procedure is developed to determine the optimal set of chart parameters(smoothing constants,error transmission function coefficients,control limits,and sampling intervals)that minimizes the out-of-control ARL over a range of shifts while constraining the in-control ARL.Extensive comparisons are made between various fixed and variable sampling interval configurations of AEWMA SR and EWMA SR control charts.The results demonstrate the superiority of the proposed VSI AEWMA SR control chart in providing robust and balanced shift detection performance across different magnitudes of shifts.Unlike individual EWMA control charts tuned for specific shifts,the AEWMA adaptation allows general sensitivity to a range of shifts.Furthermore,the VSI feature leads to substantially faster signaling times(lower out-of-control ATS values)compared to fixed-sampling charts.The paper also presents approaches to recursively calculate the probability mass functions of the run length under both in-control and out-of-control conditions.A case study on vibration acceleration monitoring data is provided,highlighting the rapidity of the VSI AEWMA SR control chart in detecting a shift compared to its fixed-sampling counterpart.In summary,this research intro-duces an effective nonparametric AEWMA control charting technique that offers robust median monitoring performance when data distributions are unknown,combines the advantages of adaptation and variable sampling intervals,and provides a comprehensive optimization and evaluation framework.The VSI AEWMA SR control chart is a valuable scheme for various applications where parametric assumptions may not hold and flexible,efficient shift detection is critical.关键词
非参数AEWMA控制图/变采样间隔/平均运行链长/平均报警时间Key words
nonparametric adaptive EWMA control chart/variable sampling intervals/average run length/average time to signal分类
数理科学引用本文复制引用
唐安安,胡雪龙,谢富鹏,孙金生..非参数自适应EWMA SR控制图及其变采样间隔设计[J].运筹与管理,2024,33(3):82-88,7.基金项目
国家自然科学基金资助项目(72101123) （72101123）
江苏省自然科学基金项目(BK20200750) （BK20200750）
江苏高校哲学社会科学基金项目(2020SJA0090) （2020SJA0090）
