Robust algorithms for economic designing of a nonparametric control chart for abrupt shift in location

The existing statistical process control procedures typically rely on the fundamental assumption of a parametric distribution of the quality characteristic. However, when there is a lack of knowledge about the underlying distribution (as full knowledge is not available in practice), the performance of these parametric charts is very likely to be heavily degraded. Motivated by this problem, a one-sided nonparametric monitoring procedure using the single sample sign statistic is proposed for detecting a shift in the location parameter of a continuous distribution. An economic model of the control chart is developed to optimize the sample size, sampling interval, and control limits. Three data-dependent estimation approaches for the unknown parameter are evaluated and discussed. Simulation results exhibit that our proposed procedure generally performs well under a great variety of continuous distributions and hence it is recommended as an alternative scheme especially when the knowledge of the underlying distribution is imperfect. Furthermore, beneficial recommendations of estimation approach selection are provided for practical implementation of the control chart.