The guaranteed adaptive c-charts with estimated parameter

The performance of control charts with estimated parameters in Phase II depends on the accuracy of parameter estimation in Phase I. Estimation accuracy depends on the amount of data. Simulation results show that no realistic number of Phase I samples is available to ensure that the in-control performance of control charts with estimated parameters is close to cases where the parameters are known. In this paper, the bootstrapping method is applied to adjust the control and warning limits of c-charts with adaptive sampling schemes, such as variable sample size, variable sampling intervals, and variable parameters. The adjusted charts guarantee that the in-control average adjusted time to signal is more than a certain amount with a predefined probability. In addition, the performance of the adjusted adaptive c-charts is compared with the commonly used approach to design adaptive c-charts.