ABSTRACT
The geometric process (GP) introduced by Lam (1988) can be used to model the occurrence of events that have an underlying monotonic trend. This type of trend can be observed in many practical problems in different areas of our everyday life, such as engineering, epidemiology, business, and health. To provide improved flexibility in modeling phenomena and situations involving monotonic trends, a variety of extensions of the GP have been proposed. This chapter provides an overview of geometric and geometric-like processes (GLPs). We include some basic definitions, facts, and references for these processes. We also provide a taxonomy of GLPs showing the connections between the various approaches taken by researchers in this area. Some of their applications in areas such as maintenance, warranty analysis, and others are also outlined with appropriate references. As a specific application of the GP we present the alternating geometric process (AGP) in which a system subject to failure experiences an alternating sequence of episodes of operation and repair. We provide some specific results for the AGP in the setting of items under warranty and illustrate the model with a real data application.
