A simulation comparison of some distance‐based EWMA control charts for monitoring the covariance matrix with individual observations

Abstract

It is common in modern manufacturing to simultaneously monitor more than one process quality characteristic. In such a multivariate scenario, the monitoring of the covariance matrix, along with the mean vector, plays an important role in assessing whether a process stays in control or not. However, monitoring the covariance matrix is technically more difficult, especially when there is only one observation available in each subgroup, disabling the usual sample covariance matrix as an effective estimator. To monitor the covariance matrix with individual observations in Phase II stage, several exponentially weighted moving average (EWMA) control charts have been constructed based on the distance between the estimated process covariance matrix and its target value.In this paper, two new control charts are devised using the sum of the square roots of the absolute deviations and its combination with the sum of squared deviations. These distance-based control charts are compared via the simulation experiments on different simulated out-of-control covariance matrices with respect to the number of quality characteristics being monitored, the shift pattern, and the shift magnitude. The simulation results identify the control charts that perform relatively robust and show that these various control charts may have their respective merits on different out-of-control scenarios.

Monitoring covariance in multivariate time series: Comparing machine learning and statistical approaches

“…More kinds of MEWMA control charts could also be tested, such as those that consider the diagonal and off-diagonal elements of the covariance matrix separately, as in Yeh et al, 49 Shen et al, 50 and Ning and Li. 51 Although Bodnar and Schmid 17 favored MCUSUM methods, we found them to be unable to maintain a consistent 𝐴𝑅𝐿 𝐼𝐶 in more complex settings. Focus could also be directed at developing a more stable MCUSUM control chart for multivariate time series.…”

“…Future research could include testing a larger variety of NNs for detrending and refining the proper structure of a GRU model, such as choices for the number of layers and activation functions, for a given process. More kinds of MEWMA control charts could also be tested, such as those that consider the diagonal and off‐diagonal elements of the covariance matrix separately, as in Yeh et al., 49 Shen et al., 50 and Ning and Li 51 . Although Bodnar and Schmid 17 favored MCUSUM methods, we found them to be unable to maintain a consistent $$ARL_{IC}$$ in more complex settings.…”

Capturing a Change in the Covariance Structure of a Multivariate Process

“…Ref. [21] develops a distribution-free control chart for this purpose, and [22,23] also refreshes the literature of methods for statistical surveillance of covariance structures with particularly developed control charts. The contribution of [24] is also a valuable contribution in literature based on machine learning approaches for the monitoring of the covariance matrix in multivariate SPC, and forms a basis for the departure of potential future studies.…”

Monitoring the covariance matrix of bivariate processes with the DVMAX control charts

“…Jing et al 19 proposed a directional covariance matrix control chart by considering that directional shifts may occur in only one independent parameter if the process is relatively stable. Ning and Li 20 proposed a simulation comparison of some distance‐based EWMA control charts for monitoring the covariance matrix with individual observations. Cabral Morais et al 21 investigated how joint schemes for the mean vector and covariance matrix are prone to trigger misleading signals.…”