Proposed variable sampling interval maximum EWMA and distance EWMA charts with unknown process parameters

The variable sampling interval (VSI) exponentially weighted moving average (EWMA) chart which varies the chart's sampling interval according to the value of the current plotting statistic increases the speed of the standard EWMA chart in detecting shifts. Joint monitoring schemes use a single combined statistic for the mean and variance in process monitoring. To simultaneously monitor the mean and variance of a process from the normal distribution, two VSI EWMA schemes with unknown process parameters, based on (i) Maximum (Max) and (ii) Distance (Dis) type combining functions, are proposed in this paper. Each of these schemes uses a single plotting statistic. The effects of parameter estimation on the performance of the proposed VSI Max EWMA and VSI Dis EWMA schemes, in terms of the average time to signal, standard deviation of the time to signal, expected average time to signal and median time to signal criteria, are studied using Monte Carlo simulation. The results show that the proposed schemes can identify process shifts quicker than the existing Max/Dis Shewhart (SH), Max/Dis cumulative sum (CUSUM) and Max/Dis EWMA schemes. The implementation of the proposed schemes is demonstrated using a commercial dataset.