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Another Look at the VSI EWMA x̄ Chart when Estimating Process Parameters

The performance of the variable sampling interval (VSI) exponentially weighted moving average (EWMA) chart is generally investigated under the assumption of known process parameters. Nevertheless, the process parameters need to be estimated from a historical Phase-I dataset because they are usually unknown in practice. When the process parameters are estimated, the chart’s performance differs among practitioners as different number of Phase-I samples is used. This leads to different parameter estimates in constructing the chart’s limits and variation in the average time to signal (ATS). This type of variation is crucial to be considered when evaluating the performance of the control chart with estimated process parameters. To consider practitioner-to-practitioner variation, this paper investigates the performance of the VSI EWMA x̄ chart with estimated process parameters by using standard deviation of the ATS. Monte Carlo simulation results show that the VSI EWMA x̄ chart requires many Phase-I samples to achieve the desired performance. The results also show that a greater number of Phase-I samples is needed for the VSI EWMA x̄ chart when the smoothing constants are large. This is because larger values of smoothing constants lead to higher variation in the run-length distribution.