BS ISO 7870-9:2020 pdf free.Control charts.Control charts for stationary processes.
BS ISO 7870-9 Many statisticians and statistical process control practitioners have found that autocorrelation in process data has an impact on the performance of the traditional SPC charts. Similar to autocovariance (see 3.1.1), autocorrelation is internal correlation between members of a series of observations ordered in time. Autocorrelation can be caused by the measurement system, the dynamics of the process, or both. In Annex B, the impact of positive autocorrelation on the performance of various traditional control charts is demonstrated.Assuming that the model is true, the residuals are statistically uncorrelated to each other. Then, traditional SPC charts such as X charts, CUSUM charts and EWMA charts can be applied to the residuals.When an X chart is applied to the residuals, it is usually called an X residual chart. Once a change of the mean in the residual process is detected, it is concluded that the mean of the process itself has been out-of-control. Similarly, the CUSUM residual chart and EWMA residual chart are proposed[2][3]. See Reference [4] for comparisons between residual charts and other control charts.Advantage of the residual charts: a residual chart can be applied to any autocorrelated data, even if it is nonstationary. Usually, a model is established with time series or other model fitting software. Disadvantages of the residual charts: the residual charts do not have the same properties as the traditional charts. The X residual chart for an AR(1) process (for an AR(1) process, see A.3.3) can have poor capability to detect a mean shift. Reference [5] shows that when the process is positively autocorrelated, the X residual chart does not perform well. Reference [6] shows that the detection capability of an X residual chart sometimes is small comparing to that of an X chart; the residual charts require time series or other modelling. The user of a residual chart shall check the validity of the model over time to reduce the mixed effect of modelling error and process change. An example is illustrated in which the data, with a size of 50, are the daily measurements of the viscosity of a coolant in an aluminium cold rolling process[7]. Figure 1 shows the data with a decreasing trend. It is suspected that the measurements are not independent. Figure 2 shows the sample autocorrelation function (ACF) for lags from 0 to 12. For sample autocorrelation and ACF, see A.4.2 and A.5 in Annex A, and Reference [8]. As indicated in A.5, under the assumption for an i.i.d. normal sequence, approximately BS ISO 7870-9 pdf download.