A new sampling strategy for the Shewhart control chart monitoring a process with wandering mean

In many processes, such as in chemical and process industries, the observations of a quality characteristic to be monitored may be correlated, if sampling intervals are short. Correlation can be modelled by considering the process mean as a random variable wandering according to an autoregressive AR1$ AR\left( 1 \right) $ model and the observations from the process modelled as the mean plus a random error due to short-term variability or measurement error. The sensitivity of the Shewhart X¯$ {\bar {X}} $ control chart in the detection of a special cause is negatively affected by presence of correlation among observations. To overcome this problem, a new sampling strategy, denoted as ESSI (Equally Spaced Samples Items), is proposed to implement the Shewhart X¯$ {\bar {X}} $ control chart as opposed to the traditional rational subgrouping approach. The ESSI sampling strategy allows observations belonging to the same sample to be collected from the process at equally spaced time intervals between two successive inspections. A numerical analysis shows that the implementation of the ESSI strategy in presence of a process wandering mean significantly improves the statistical performance of the Shewhart X¯$ {\bar {X}} $ control chart vs. rational subgrouping for different levels of autocorrelation. Furthermore, by implementing the ESSI sampling strategy, the selection of the width of control limits for the control chart is independent of the correlation. An illustrative example shows the implementation of the proposed strategy.