Background on Coherent Systems

We will use the term “system” quite freely and regularly, even though it will remain an undefined term throughout this monograph. As we all have some experience with engineered “systems,” our use of the term should cause no confusion. Informally, we can think of a system as consisting of a collection of “components,” basic constituents which are connected in some fashion to create the whole. We might consider a radio, an automobile, a computer or a cell phone as concrete examples of systems in common use. The main characteristic of our use of the term is that a system works or fails to work as a function of the working or failure of its components. While there are various ways to formalize the notion of a system being partially functioning (for example, a car could technically be driven for a few miles with a flat tire), we will follow the convention established by Birnbaum et al. [9] and consider a system to be either working or failed at any given point in time. To quantify this fact, we assign a 1 to the event that the system works and a 0 to the event that the system fails. The same can be said of each component.