The stochastic process has a number of states that describe the behaviour of a set of random variables. The behaviour of the stochastic process varies with respect to an index. In reliability engineering, the index is generally system time. This means that the stochastic process is used to describe the dynamics of a system with respect to time.

State space is the set of all possible states of a process, and index space is a set of all possible index values. At a particular time (index value), a system will be in one of its possible states. In each state, a set of events can occur. The occurrence distribution of each state depends on the history of the system (all previous events and state transition times).

In reliability engineering, the state space is generally discrete. For example, a system might have two states: good and failed. There are, however, applications in which state space can be continuous. Examples include the water level in a tank (where tank failure characteristics depend on the water level), the load on a shaft, the waiting time for repair, etc.. If the state space is discrete, then the process is called a chain.

Similarly, the state index can be discrete or continuous. In most reliability engineering applications, the state index (time scale) is continuous, which means that component failure and repair times are random variables. However, cases exist where the state index is discrete. Examples include time-slotted (synchronous) communication protocol, shifts in equipment operation, etc..

Given a continuous-time process, it is often useful to embed a discrete time process by considering only those points at which certain events (like state changes) happen within the process. In such an embedded process, the discrete points are generally not equally spaced in real time. However, such details are not included in this document.