EWMA control chart limits for first‐ and second‐order autoregressive processes

Abstract

Today's manufacturing environment has changed since the time when control chart methods were originally introduced. Sequentially observed data are much more common. Serial correlation can seriously affect the performance of the traditional control charts. In this article we derive explicit easy-to-use expressions of the variance of an EWMA statistic when the process observations are autoregressive of order 1 or 2. These variances can be used to modify the control limits of the corresponding EWMA control charts. The resulting control charts have the advantage that the data are plotted on the original scale making the charts easier to interpret for practitioners than charts based on residuals.

Defining the structure of DPCA models and its impact on process monitoring and prediction activities

“…Operation Conditions (NOC) region is no longer valid under these circumstances, and several alternative methodologies were proposed to the classic univariate [1][2][3], multivariate [4][5][6] and mega-variate [7][8][9][10] approaches. These can be organized into three distinct classes of methods: i) methods based on correcting/adjusting control limits for the existent SPM methods, using knowledge of the specific dynamical model underlying data generation [11]; ii) methods based on time series modelling followed by the monitoring of one-step-ahead prediction residuals [12,13]; iii) methods based on time-domain variable transformations, that diagonalize, in an approximate way, the autocorrelation matrix of process data [14,15].…”

Industrial Process Monitoring in the Big Data/Industry 4.0 Era: from Detection, to Diagnosis, to Prognosis

“…characteristic of static stationary processes, including all Shewhart-like control charts and its multivariate generalizations, such as the Hotelling's T 2 control chart and Multivariate Statistical Process Control based on Principal Components Analysis (PCA-MSPC), have to be upgraded to include process dynamics [30]. Several types of solutions were proposed to handle the presence of autocorrelation in continuous production systems, namely: (i) adjusting the control limits of the monitoring charts-a solution essentially restricted to univariate processes with very simple dynamics (such as univariate first order autoregressive processes) [31][32][33]; (ii) monitoring the one-step-ahead prediction residuals using a dynamic model structure estimated from normal operation data, such as; time-series [30,34], state-space (e.g., through Canonical Variate Analysis) [35][36][37][38] or dynamic latent variable models [39][40][41]; (iii) implement a variable transformation that diagonalizes the autocorrelation matrix, as happens in multiscale statistical process control; this approach also allows one to handle the presence of multiscale dynamics and complex disturbances [42][43][44][45].…”

Fault Detection in Continuous and Periodic Industrial Chemical Processes with Hidden Markov Models

“…It can be checked by a correlogram of the sample autocorrelation function (ACF). To handle this issue, time-series modeling [17,18], control limits correction [19], and variable transformation [20,21], may be adopted. The first approach was used in this work with the identification of an autoregressive (AR) model (others can be used as the ARMA model) over the monitoring metric calculated onto the validation data.…”

“…The resulting normal and independent residuals can then be used as a monitoring statistic in a Shewhart-type control chart. There is also the chance to directly use the HMM output as the monitoring metric not employing a residuals approach [23].…”