Multivariate Quality Control Chart for Autocorrelated Processes

Abstract

Traditional multivariate statistical process control (SPC) techniques are based on the assumption that the successive observation vectors are independent. In recent years, due to automation of measurement and data collection systems, a process can be sampled at higher rates, which ultimately leads to autocorrelation. Consequently, when the autocorrelation is present in the data, it can have a serious impact on the performance of classical control charts. This paper considers the problem of monitoring the mean vector of a process in which observations can be modelled as a first-order vector autoregressive VAR (1) process. We propose a control chart called Z-chart which is based on the single step finite intersection test (Timm, 1996). An important feature of the proposed method is that it not only detects an out of control status but also helps in identifying variable(s) responsible for the out of control situation. The proposed method is illustrated with the help of suitable illustrations.Multivariate statistical process control, autocorrelation,

Multivariate statistical process control charts: an overview

“…Woodall et al 64 discussed the general issue involved in using control charts to monitor processes, which is better characterized by a relationship between a response variable and one or more explanatory variables. Also, Kalgonda and Kulkarni 65 proposed a multivariate quality control chart for autocorrelated processes in which observations can be modeled as a first-order autoregressive process.…”

Multivariate Control Charts Based on Bayesian State Space Models

“…As stated before univariate control charts for autocorrelated processes have been discussed in the literature (Montgomery 1 , Box and Luceñno 2 ), however, for multivariate processes the general focus has been placed to uncorrelated processes. Dyer et al 20 , Jiang 21 , Kalgonda and Kulkarni 22 and Noorossana and Vaghefi 23 consider multivariate control charting for autocorrelated processes based on autoregressive-moving-average (ARMA) time series models and the T 2 and multivariate CUSUM control charts are illustrated. Pan and Jarrett 24 build a multivariate T 2 control chart for the forecast errors of the process.…”

The effect of the autocorrelation on the performance of the T 2 chart

“…A recent study dealing with the estimation of the mean vector is in (Wang, Huwang, & Yu, 2015). According to Kalgonda and Kulkarni (2004), the cross covariance matrix of X t has the following property: = + . After some algebra we obtain…”

“…However, in many applications the dynamics of the process induce correlation in observations that are closely spaced in time. The autocorrelation has a serious impact on the performance of conventional control charts (Kalgonda & Kulkarni, 2004). Recently, Du and Lv (2013) proposed a control chart based on the minimal Euclidian distance to detect mean shifts in autocorrelated processes.…”