
The double sampling (DS) X chart is superior to the traditional Shewhart X chart in detecting small and moderate process mean shifts. In general, the DS X 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 X 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 X chart with estimated parameters, so that satisfactory performances as the case with known parameters are attained.
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