BS ISO 7870-9:2020 pdf download.Control charts Part 9: Control charts for stationary processes.
4.3.2 Modified CUSUM chart
Reference [1.21 considers charting the raw data directly by a C[JSLJM chart when the process autocorrelation is low. When the autocorrelation is high, the use of transformed observations is considered. Other approaches are proposed to apply modified CUSUM charts to AR(1) processes or some other time seriesI9lIl3l.
4.4 Comparisons among charts for autocorrelated data
There are comparisons among some control charts for autocorrelated data. References 191 and 141 compare the Xchart, Xresidual chart, CUSLJM residual chart, EWMA residual chart, and EWMAST chart for stationary AR(1) processes by simulations. The EWMAST chart performs better than the CUSIJM residual and EWMA residual charts. Overall, it also performs better than the X chart and X residual chart. The comparisons also show that the CUSUM residual and EWMA residual charts perform almost the same. The CUSUM residual and EWMA residual charts perform better than the X residual chart when the process autocorrelation is not strong. On the contrary, when the autocorrelation is strong, the X residual chart performs better than the other residual charts. When the process autocorrelation is very strong, i.e. the process is near nonstationary, the IWMAST chart still performs relatively better than other charts.
An obvious advantage of using EWMAST chart is that there is no need to build a time series model for stationary process data. The implementation of an EWMAST chart only requires the estimation of the process mean, standard deviation, and autocorrelations obtained when the process is under control. In summary, when the process is autocorrelated and stationary, it is recommended to use EWMAST chart to monitor the process mean.
6 Other approaches to deal with process autocorrelation
In CLuse 4 and Clause 5. various process control charts to accommodate the autocorrelation of the process data are discussed. As an alternative to accommodating, the effect of the autocorrelation can be reduced by some data treatment mechanism. Reference 1171 discusses the effects of the choice of the sampling interval on some process data. When the process is stationary and the samples are taken less frequently in time, the autocorrelation of the sampled data decreases. Thus, when the sampling interval is sufficiently large, the data appear to be uncorrelated. However, this approach discards the intermediate data and therefore increases the possibility of missing important events in the process. Instead of choosing a large sampling interval, moving averages of process with a fixed window size can be formed. Reference L1I shows that, when a process is stationary and satisfies some regularity conditions, the non-overlapping means or batch means are asymptotically independent and normally distributed. Thus, when the batch size is large enough, the batch means can be treated as white noise. For some specific stationary processes, numerous papers discuss the process behaviour of the subsample means or batch means, and the related charts for batch means. In Reference 1191. the effect of using generalized moving averages of a stationary process to reduce its autocorrelation and its applications to process control charts are discussed.BS ISO 7870-9 pdf download.