The recurrent event process of a success preceded by a failure and its application

We describe a simple discrete time renewal process of an event where a success is preceded by a failure. Its properties, especially the distributions of the counting and the interval processes, are investigated. We also propose an application to statistical process control based on the waiting time between two adjacent events. It is shown that the average number inspected under the new control scheme is larger than with the so-called CCC control chart.