A re-evaluation of the run rules xbar chart when the process parameters are unknown

ABSTRACT Run Rules chart are often implemented for process monitoring. The process observations are usually assumed normally distributed, and the process parameters are assumed known. In fact, a very limited number of Phase I samples may only be available to the practitioners to estimate the process parameters, the control chart's properties will vary among different practitioners. Considering this variability, the performance of the Run Rules chart with estimated parameters is investigated. To measure this variability, the standard deviation of average run length (SDARL) is used to evaluate the performance of control chart. The results show that the Run Rules chart requires a much larger amount of Phase I data to sufficiently reduce the between-practitioners variability. Moreover, we also investigate the properties of Run Rules chart with estimated parameters under the non-normal distributed data. Due to the limitation of the amount of Phase I data set in practice, a bootstrap method is applied to design the Run Rules chart. Finally, an example is provided to illustrate the application of the Run Rules chart with estimated parameters.

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