Control Charts for Monitoring Time-Between-Events-and-Amplitude Data

Abstract

In recent years, several control charts have been developed for the simultaneous monitoring of the time interval T and the amplitude X of events, denoted as the TBEA (Time Between Events and Amplitude) charts. In general, a decrease in T and/or an increase in X can result in a negative, hazardous or disastrous situation that needs to be efficiently monitored with control charts. The goal of this chapter is to further investigate several TBEA control charts and to hopefully open new research directions. More specifically, this chapter will (1) introduce and compare three different statistics, denoted as Z1, Z2 and Z3, suitable for monitoring TBEA data, in the case of four distributions (gamma, lognormal, normal, and Weibull), when the time T and the amplitude X are considered as independent, (2) compare the three statistics introduced in (1) for the same distributions, but considering that the time T and the amplitude X are dependent random variables and the joint distribution can be represented using Copulas and (3) introduce a distribution-free approach for TBEA data coupled with an upper-sided EWMA scheme in order to overcome the “distribution choice” dilemma. Two illustrative examples will be presented to clarify the use of the proposed methods.