A Variable Sampling Interval Multivariate Exponentially Weighted Moving Average Control Chart Based on Median Time-to-Signal

Abstract

In this study, the median time-to-signal (MTS) is used as an alternative measure to the average time-to-signal (ATS) in evaluating the performance of the variable sampling interval (VSI) multivariate exponentially weighted moving average (MEWMA) chart. Although the ATS is one of the most commonly used performance measures when the sampling interval is varied, it is not an accurate representation of the entire time-to-signal distribution of the VSI charts. Therefore, the percentage points (percentiles) of the time-to-signal distribution are provided for a more comprehensive study of the VSI MEWMA chart. A Monte Carlo simulation is used to calculate the MTS values for various magnitudes of shifts in the process mean vector. The optimal design strategy is to find the charting parameters having the minimum out-of-control MTS (MTS1). A comparison study shows that the VSI MEWMA chart is more effective than the standard MEWMA chart with fixed sampling interval, in detecting shifts in the process mean vector in terms of the MTS.