A preliminary study on the double sampling X-bar chart with unknown parameters

The double sampling (DS) X̅ chart is superior to the traditional Shewhart X̅ chart in detecting small and moderate process mean shifts. In general, the DS X̅ chart is typically designed under the assumption of known parameters. Nevertheless, the actual process parameters are rarely known in practice and are usually estimated from an in-control reference Phase I sample. In this paper, we discuss the effects of parameter estimation on the performance of the DS X̅ chart, for both the in-control and out-of-control situations. It is found that the in-control and out-of-control performances are significantly different from the case when parameters are known, especially when the shifts and the sample sizes are small. In light of these unfavorable performances, the Phase-I sample-size recommendations are provided for practitioners in designing the DS X̅ chart with estimated parameters, so that satisfactory performances as the case with known parameters are attained.