A new nonparametric scheme for simultaneous monitoring of bivariate processes and its application in monitoring service quality

Abstract

We consider a new nonparametric control chart for monitoring bivariate processes based on a distance measure. This statistic was originally introduced in context of a strictly nonparametric bivariate test for two-sample location problem and was shown to be more powerful than several competitors including Hotelling’s T² in a large number of situations. Our proposed scheme is useful in simultaneous monitoring of the event frequency and magnitude, call centre response times and its service quality or time between the two major earthquakes and the magnitude in Richter scale, etc. Unlike most of the traditional approaches for simultaneous monitoring of event frequency and magnitude that consider event frequency and magnitude are independent, our proposed chart takes into account the dependence between two variables. We consider that the frequencies are large enough and the two variables are continuous, but we make no assumption about the mathematical form of the process distribution. We consider the availability of a Phase-I data. We discuss the design and implementation procedure in details. We conduct some Monte-Carlo simulation to examine various properties of the proposed scheme. We also illustrate our proposed scheme with a real data.

Keywords:

• Bivariate process
• call centre
• Mathur statistic
• Monte-Carlo
• nonparametric
• Phase-II
• ranks
• service quality
• Shewhart chart