A class of distribution-free one-sided Cucconi schemes for joint surveillance of location and scale parameters and their application in monitoring cab services

Abstract

Simultaneous distribution-free surveillance (SDFS) of location and scale parameters of a process based on a single plotting statistic has emerged as a prevalent research issue in the past seven years. Most of the SDFS schemes are, however, appropriate for monitoring two-sided shifts in location-scale. In monitoring service quality or time to an event, among others, decreasing process median or variability are usually considered as a process improvement and not something to worry about in practice. We only desire to have a quick signal when there is an increase in the median or scatter as they refer to a deterioration in the process quality. On the contrary, in network traffic surveillance, a decrease in process variability could be a matter of concern as it may result in network congestion where a decreasing shift may be of more interest. In such instances, specific one-sided shifts are of more importance, and a one-sided SDFS scheme would be more appropriate than traditional two-sided schemes. In this article, we propose several Shewhart-Cucconi type SDFS schemes for jointly monitoring one-sided deviations in location or scale or both parameters of a process. We discuss the implementation steps and establish the in-control robustness of the new surveillance plans. We compare proposed schemes with existing one-sided Shewhart-Lepage type schemes using run-length properties. Numerical results substantiate that the proposed schemes perform quite well in many cases. We explain the application of newly designed schemes in surveillance of waiting time during a taxi ride in some cities.