Abujiya Mu'azu Ramat, Riaz Muhammad, Lee Muhammad Hisyam
Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Skudai, Johor, Malaysia; Preparatory Year Mathematics Program, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia.
Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia.
PLoS One. 2015 Apr 22;10(4):e0124520. doi: 10.1371/journal.pone.0124520. eCollection 2015.
The cumulative sum (CUSUM) control chart is widely used in industry for the detection of small and moderate shifts in process location and dispersion. For efficient monitoring of process variability, we present several CUSUM control charts for monitoring changes in standard deviation of a normal process. The newly developed control charts based on well-structured sampling techniques - extreme ranked set sampling, extreme double ranked set sampling and double extreme ranked set sampling, have significantly enhanced CUSUM chart ability to detect a wide range of shifts in process variability. The relative performances of the proposed CUSUM scale charts are evaluated in terms of the average run length (ARL) and standard deviation of run length, for point shift in variability. Moreover, for overall performance, we implore the use of the average ratio ARL and average extra quadratic loss. A comparison of the proposed CUSUM control charts with the classical CUSUM R chart, the classical CUSUM S chart, the fast initial response (FIR) CUSUM R chart, the FIR CUSUM S chart, the ranked set sampling (RSS) based CUSUM R chart and the RSS based CUSUM S chart, among others, are presented. An illustrative example using real dataset is given to demonstrate the practicability of the application of the proposed schemes.
累积和（CUSUM）控制图在工业中广泛用于检测过程位置和离散度的小幅度和中等幅度变化。为了有效地监测过程变异性，我们提出了几种用于监测正态过程标准差变化的CUSUM控制图。基于结构良好的抽样技术——极端排序集抽样、极端双重排序集抽样和双重极端排序集抽样——新开发的控制图显著增强了CUSUM图检测过程变异性中广泛变化的能力。针对变异性中的点偏移，根据平均运行长度（ARL）和运行长度的标准差评估了所提出的CUSUM尺度图的相对性能。此外，为了评估整体性能，我们采用了平均比率ARL和平均额外二次损失。还给出了所提出的CUSUM控制图与经典CUSUM R图、经典CUSUM S图、快速初始响应（FIR）CUSUM R图、FIR CUSUM S图、基于排序集抽样（RSS）的CUSUM R图和基于RSS的CUSUM S图等的比较。给出了一个使用真实数据集的示例来说明所提出方案应用的实用性。
