The variable sampling rate X̄ control charts for monitoring autocorrelated processes

Abstract

Recent studies demonstrated that the adaptive X control charts are more efficient than fixed parameters (FP) X control chart from statistical and economic criteria.The usual assumption for designing a control chart is that the observations from the process are independent. However, for many processes, such as chemical processes, consecutive measurements are often highly correlated, especially when the interval between samples is small. In the present paper, the observations are modeled as an AR(1) process plus a random error, and the properties of the variable sampling rate (VSR) X charts are evaluated and studied under this model. Based on the study, the VSR X chart is faster than the FP, variable sampling interval and variable sample size X control charts in detecting mean shifts. However, when the level of autocorrelation is high or the process mean shift is large, the advantage of the VSR X chart is reduced.

Adaptive Control Charts: Recent Developments and Extensions

“…The most typical approach is to fit appropriate time‐series models to the observations and then charting the residuals. Recently, this method was applied by Costa and Claro, Lin and Chou, Zou et al , and Costa and Machado …”

“…The same model applied by Zou et al is used by Lin and Chou to formulate a process with autocorrelated observations. However, the schemes investigated do not include sampling at fixed times.…”

“…Zou et al choose the EWMA chart based on the residuals from the forecast values of the model and concluded that when the level of autocorrelation is high, the VSIFT chart performs uniformly better than the EWMA chart. On the contrary, Lin and Chou compared the VSR chart with the traditional EWMA chart. They concluded that the VSR chart is not as good as the EWMA chart in detecting small shifts, especially when correlation is high.…”

“…The most typical approach is to fit appropriate time-series models to the observations and then charting the residuals. Recently, this method was applied by Costa and Claro, 24 Lin and Chou, 25 Zou et al, 26 and Costa and Machado. 27 Zou et al 26 suggest a variable sampling scheme at fixed times, including the VSI and VSSI schemes, to enhance the efficiency of the X chart for autocorrelated process.…”

TheT2chart with mixed samples to control bivariate autocorrelated processes

“…In other studies with single variables, the AR (1) model has been used to describe a natural movement of the process mean (Reynolds, Arnold, and Baik 1996;Reynolds 1999, 2001;Lin and Chou 2008;Zou, Wang, and Tsung 2008;Lin 2009;Costa and Machado 2011;Franco, Costa, and Machado 2012). When the process mean wanders neither the skip nor the mixed sampling strategies reduce the effect of the autocorrelation on the X chart's performance.…”