Guaranteed in-control performance of the synthetic (X)over-bar chart with estimated parameters

Control charts are usually investigated under the assumption of known process parameters. In practice, however, the process parameters are rarely known and they have to be estimated from different Phase I data sets. The properties of control charts with estimated parameters are usually investigated with the unconditional average of the average run length. Control chart's performance is known to vary among practitioners because of the use of different Phase I data sets. Considering the between-practitioners variability in control chart's performance, the standard deviation of the average run length is developed to reevaluate the properties of the synthetic X chart with estimated parameters. Because of the limited amount of Phase I data in practice, the bootstrap method is used as a good adjustment technique for the synthetic chart's parameters.