Monitoring autocorrelated processes using variable sampling schemes at fixed-times

Traditional control charts for process monitoring are based on taking samples of fixed size from the process using a fixed sampling interval. A recent development in control charts is the use of adaptive control charts, i.e. the variable sampling interval (VSI) and variable sampling size charts. This paper extends this idea to the autocorrelated process. We consider a time series model which is a first-order autoregressive process plus a random error. With variable intervals, the sampling time may be inconvenient, so using only two intervals, referred to as 'variable sampling interval at fix times' makes the method easier to use in practice. The sampling rate can also be adjusted by the number of samples collected, VSRFT, for 'variable sampling rate at fixed times'. We study what we call 'variable sampling at fixed times', VSFT, which includes both VSIFT and VSRFT schemes, using a Markov chain model and integral equations. We show that our methods detect process shifts faster, on average, than fixed sampling X-bar charts, and at least comparable detection ability with the less practical VSI charts.