Some distribution-free Lepage-type schemes for simultaneous monitoring of one-sided shifts in location and scale

Abstract

Abstract From monitoring network traffic to health care systems, product quality to customer satisfaction, system reliability to certain economic parameters, Statistical Process Monitoring (SPM) schemes are widely used as an important statistical tool. Many of the complex processes have unknown or complicated distributions, where distribution-free process monitoring techniques are recommended. In the present world, it is important to monitor both the process location, for example, median, and the process scale as a measure of variability. In recent years, several distribution-free process monitoring schemes are introduced in the literature to monitor both the location and scale parameters simultaneously. Interestingly, however, all these schemes are intended for two-sided shifts in location-scale. More often, only one-sided shifts are important. For example, in a manufacturing industry, usually the reduction in variation of forged piston rings is welcome and we only need to monitor an increase in variation. On the other hand, in the context of network traffic, a low variation may lead to network congestion and needs to be monitored. To this end, we introduce a class of Shewhart-Lepage type schemes for monitoring one-sided shifts. We also investigate performances of the various schemes and compare them in terms of run length properties, such as mean, standard deviation, median and some percentiles. We carry out large scale Monte-Carlo simulation and our computational findings are extremely encouraging. We illustrate the implementation of the proposed chart using two sets of real data.