Monitoring of serially correlated processes using residual control charts

Abstract

Abstract. Control charts act as the most important tool for monitoring of process parameters. The assumption of independence that underpins the implementation of the charts is violated when process observations are correlated. The e ect of this issue can lead to the malfunctioning of the usual control charts by causing a large number of false alarms or slowing the detection ability of the chart in unstable situations. In this paper, we investigated the performance of the Mixed EWMA-CUSUM and Mixed CUSUM-EWMA charts for the e cient monitoring of autocorrelated data. The charts are applied to the residuals obtained from tting an autoregressive (AR) model to the autocorrelated observations. The performance of these charts is compared with the performances of the residual Shewhart, EWMA, CUSUM, combined Shewhart-CUSUM, and combined Shewhart-EWMA charts. Performance criteria such as Average Run Length (ARL) and Extra Quadratic Loss (EQL) are used for the evaluation and comparison of the charts. Illustrative examples are presented to demonstrate the application of the charts to serially correlated observations.

On bivariate control charts for the mean of autocorrelated process

“…Abbas et al (2013) and Zaman et al (2014) proposed the mixed EWMA-CUSUM (MEC) and mixed CUSUM-EWMA (MCE) charts, respectively, for monitoring processes for which the observations are independent and normally distributed. Osei-Aning et al (2017) showed that these charts malfunction in the presence of serial correlation by producing frequent false alarms. Harris and Ross (1991) discussed the effect of autocorrelation on the CUSUM and EWMA charts in several different correlation structures and, for these charts, calculated the mean and distribution of run length (RL) of the sequence.…”

An integrated model for optimal selection of quality, maintenance, and production parameters with auto correlated data

“…In addition to the introduced approaches, neural network-based control charts can also be categorized as the third approach in which the data are processed without necessity of identifying models or making adjustments [12]. Some recent studies using different approaches can be referred to in [13][14][15].…”