Nonparametric control of the conditional performance in statistical process monitoring

Because the in-control distribution and parameters are generally unknown, control limits have to be estimated using a Phase I reference sample. Because different practitioners obtain different samples, their control limit estimates will vary and, consequently, also their control chart performance. We propose the use of nonparametric tolerance intervals in statistical process monitoring to guarantee a minimum control chart performance with a prespecified probability. We evaluate the performance of the proposed limits for various distributions and sample sizes. Note that this nonparametric set-up includes control charts for location and dispersion. Moreover, we compare the performance with other existing methods involving data transformations and a bootstrap procedure. It turns out that the use of nonparametric tolerance intervals performs very well in statistical process monitoring, especially when moderately large sample sizes are available in Phase I.