Proposed nonparametric runs rules Lepage and synthetic Lepage schemes

Abstract

The average daily customer waiting time in a service centre is one of the most important metrics to measure performance or service quality. The average daily waiting time should meet a prespecified quality standard. Therefore, it is crucial to monitor such waiting times at regular intervals to maintain and improve the service quality. Similar problems arise in many time-between-event monitoring problems. This paper suggests two improved nonparametric Lepage schemes supplemented with runs rules, i.e., the 2-of-3 runs rules Lepage and the synthetic Lepage schemes. We show the real-life usage of the suggested schemes in monitoring the average daily customer waiting time of a service centre in Australia. The distribution-free nature of the suggested schemes allows broader applicability irrespective of the underlying process density. Moreover, the proposed schemes can jointly monitor the process location and scale parameters. We demonstrate the superiority of the suggested runs rules schemes to those without runs rules, i.e., the Shewhart-Lepage (SL) scheme through computer-intensive Monte-Carlo simulation. In general, we recommend the 2-of-3 runs rules Lepage scheme due to its efficiency and simplicity.