Distribution-free Phase-I scheme for location, scale and skewness shifts with an application in monitoring customers' waiting time.

Phase-I analysis of historical data from a statistical process is a strategic problem in Statistical Process Monitoring and control. Before the establishment of process stability, it is challenging to model historical data. Consequently, a distribution-free approach is a natural choice in Phase-I monitoring. Existing distribution-free Phase-I control charts are suitable for detecting instability in location and scale parameters only and are often insensitive in complex processes involving skewness or shape parameters. A new Phase-I control chart is proposed to identify more general shifts, including location, scale and skewness. The proposed Phase-I scheme is efficient in such a situation. The proposed Phase-I scheme uses subsamples, and the plotting statistic is based on the omnibus multi-sample linear rank statistic corresponding to the location, scale and skewness shifts. The new scheme can identify subsamples that are not in control, and it can also indicate one or more process parameters where a deviation has occurred. The encouraging performance of the proposed scheme is established with a large-scale numerical study based on Monte-Carlo in detecting shifts of various nature in a comprehensive class of situations. An illustration based on monitoring the waiting time data from a customer service centre is given. Some concluding remarks and some future research problems are also offered.