Exponentially weighted moving average Lepage-type schemes based on the lower-order percentile of the run-length metrics and their use in monitoring time-occupancy in Google applications

Abstract

Many existing monitoring schemes in the literature are based on the in-control (IC) average or median run-length. Several Phase-II schemes frequently fail to protect against the high rate of early false alarms. The problem may worsen when the average run-length metric is used, and the scheme is based on unknown and estimated parameters. Early false alarms can be avoided using monitoring schemes based on the lower-order percentiles of the IC run-length distribution. The exponentially weighted moving average (EWMA)-Lepage scheme is presented in this paper. The new design is based on a percentile-based approach that can effectively reduce and control the rate of early false alarms. The run-length properties of the EWMA scheme with the lower-order percentile-based design were investigated and compared with the double EWMA-Lepage and homogeneously weighted moving average-Lepage schemes. Detailed simulation studies show no clear winner among the three schemes for given sample sizes for the unknown shift. Instead, the size of the Phase-I and Phase-II samples heavily influences the choice of a potentially beneficial scheme. A case study on monitoring the time occupation of users on the Google application is presented to demonstrate the design and implementation of lower-percentile-based techniques. Some future research directions are offered.