A distribution-free tabular CUSUM chart for autocorrelated data

A distribution-free tabular CUSUM chart called DFTC is designed to detect shifts in the mean of an autocorrelated process. The chart's Average Run Length (ARL) is approximated by generalizing Siegmund's ARL approximation for the conventional tabular CUSUM chart based on independent and identically distributed normal observations. Control limits for DFTC are computed from the generalized ARL approximation. Also discussed are the choice of reference value and the use of batch means to handle highly correlated processes. The performance of DFTC compared favorably with that of other distribution-free procedures in stationary test processes having various types of autocorrelation functions as well as normal or nonnormal marginals.     

Controlling autocorrelated data in multistage manufacturing processes with an application to textile industry

In recent years, much attention has been given to monitoring multistage processes in order to effectively improve the product reliability. To this end, the output of the process is investigated under special circumstances, and the values corresponding to reliability‐related quality characteristic are measured. However, analyzing reliability data is quite complicated because of their unique features such as being censored and obeying nonnormal distributions. A more sophisticated picture arises when the observations of the process are autocorrelated in some cases, which makes the application of previous control procedures futile. In this paper, the accelerated failure time (AFT) regression models have been modified in order to account for autocorrelated data. Then, a cumulative sum (CUSUM) control chart and an exponentially weighted moving average (EWMA) control chart based on conditional expected values have been proposed to monitor the quality variable with Weibull distribution while taking the effective covariates into consideration. Extensive simulation studies reveal that the CUSUM control chart outperforms its counterpart in detecting out‐of‐control conditions. Finally, a real case study in a textile industry has been provided to investigate the application of the CUSUM control scheme.     

Detecting mean increases in zero truncated INAR(1) processes

Count data with zero truncation are common in the production process. It's essential to monitor these data during production flow, production quality control and market management. Most of the previous studies were based on the independent observations assumption. In fact, serial dependence of count data which significantly affects the performance of the control charts exists extensively in practice. Motivated by this, several important first-order integer-valued autoregressive time series processes are used to model the autocorrelated count data with zero truncation. We investigate the effectiveness of three following charts, the combined jumps chart, the exponentially weighted moving average chart and the cumulative sum chart, to detect the upward shifts of the process mean based on these models. A bivariate Markov chain approach could be used to obtain the average run length of these charts. Design recommendations for achieving robustness are provided based on the computation study. An application to product quality complaints data is presented to demonstrate good performances of the charts.     

基于GRU神经网络的自相关过程残差控制图

为提升自相关过程监控的效率,提出基于门控循环单元(gated recurrent unit,GRU)神经网络的自相关过程残差控制图。采用受控下的自相关过程数据对GRU网络进行离线训练与测试,对预测误差进行监控,形成控制用残差控制图。采用训练好的GRU网络预测当前过程波动,利用控制用残差控制图判定当前过程是否失控。运用蒙特卡洛仿真法,与基于一阶自回归模型、BP神经网络以及支持向量回归构建的残差控制图进行性能对比。研究表明,过程受控时,所提残差控制图与其他3种的稳态平均运行链长相差不大,即4者的性能表现相当;而在均值偏移异常过程中,所提残差控制图的平均运行链长远小于其他3种,对自相关过程均值偏移具有较好的监控性能。     

基于马尔可夫链模型的B&L VP 控制图统计性能分析

在已有VP 控制图基础上,增加了B&L转换规则,构建了基于马尔可夫链模型的B&L VP 控制图统计性能分析模型,给出了统计性能指标ATS、AATS以及ANSW的表达式。针对2组设计参数,将构建的模型与现有VP 控制图进行了比较分析,结果表明当平均运行时间相同时,本文构建的模型在缩短报警时间和减少转换次数方面,都有着明显的优势,而且随着转换参数L的增大,这种优势会增大。