Cusum of Q chart with variable sampling intervals for monitoring the process mean

Recently, adaptive control charts (that is, with variable sample sizes and/or sampling intervals) for univariate or multivariate quality characteristics have received considerable attention in Phase II analysis in the literature. Due to insufficient samples to obtain good knowledge of the parameters in the start-up process, adding adaptive features to self-starting control charts remains an open problem. In this paper, we propose an adaptive Cusum of Q chart with variable sampling intervals for monitoring the process mean of normally distributed variables. A Fortran program is available to assist in the design of the control chart with different parameters. The effect of the control chart parameters on the performance is studied in detail. The control chart is further enhanced by finding adaptive reference values. Due to the powerful properties of the proposed control chart, the Monte Carlo simulation results show that it provides quite satisfactory performance in various cases. The proposed control chart is applied to a real-life data example to illustrate its implementation.