Comparison of fixed versus variable sampling interval Shewhart x control charts in the presence of positively autocorrelated data

Shewhart x control charts are designed to be used with independent observations. Actual data are, however, often positively autocorrelated. This simulation study compares the performance of the traditional fixed interval Shewhart x control chart with the variable interval technique when the data are autocorrelated. Samples of size 1 are employed in the investigation which is conducted by varying the interval length, autocorrelation parameter, and shift in the process mean. Adjustments for false alarms caused by the presence of autocorrelation are implemented. The results suggest that the average time to signal depends on the shift magnitude and the amount of autocorrelation in the process. We show that, in general, when monitoring an autocorrelated process it is advantageous to use the variable interval technique over the fixed interval approach and that this advantage increases in proportion to the shift in the process mean.