A comparison between the performances of double sampling X and variable sample size X charts

The double sampling (DS) X and variable sample size (VSS) X charts are very effective to detect small and moderate shifts in the process mean. Both charts are usually investigated under the assumption of known process parameters. However, the process parameters are commonly estimated from an in-control Phase-I dataset because they are usually unknown in practice. Therefore, both cases of known and estimated process parameters for the DS X and VSS X charts are considered in this paper. It is well known that the run length distribution of a control chart is highly skewed, especially when the process parameters are estimated and the process is in-control or slightly out-of-control. Interpretation based solely on a specific performance measure could be misleading. Thus, various performance measures need to be used to evaluate the properties of the control charts. Generally, the design of a control chart with estimated process parameters is proposed without comparing with other control charts. Accordingly, this paper focuses mainly on the comparison of the average run length (ARL), standard deviation of the run length (SDRL) and average sample size (ASS) between the DS X and VSS X charts with known and estimated process parameters. The ARL and SDRL results indicate that the DS X chart outperforms the VSS X chart for all ranges of shifts. However, the converse is true in terms of the ASS