A distribution-free EWMA control chart for monitoring time-between-events-and-amplitude data.

Many control charts have been developed for the simultaneous monitoring of the time interval between successive occurrences of an event E and its magnitude . All these TBEA (Time Between Events and Amplitude) control charts assume a known distribution for the random variables and . But, in practice, as it is rather difficult to know their actual distributions, proposing a distribution free approach could be a way to overcome this 'distribution choice' dilemma. For this reason, we propose in this paper a distribution free upper-sided EWMA (Exponentially Weighted Moving Average) type control chart, for simultaneously monitoring the time interval and the magnitude of an event. In order to investigate the performance of this control chart and obtain its run length properties, we also develop a specific method called 'continuousify' which, coupled with a classical Markov chain technique, allows to obtain reliable and replicable results. A numerical comparison shows that our distribution-free EWMA TBEA chart performs as the parametric Shewhart TBEA chart, but without the need to pre-specify any distribution. An illustrative example obtained from a French forest fire database is also provided to show the implementation of the proposed EWMA TBEA control chart.