Full article In this paper, we investigate the reliability and stochastic properties of an n-component network under the assumption that the components of the network fail according to a counting process called a geometric counting process (GCP). Some mixture representations for the network reliability are obtained in terms of signature of the network and the reliability function of the arrival times of the GCP.
Familiar examples of time series include stock market and exchange rate fluctuations, signals such as speech, audio and video; medical data such as a patient's EKG, EEG, blood pressure or temperature; and random movement such as Brownian motion or random walks.
Examples of random fields include static images, random topographies (landscapes), or composition variations of an inhomogeneous material.
In the mathematics of probability, a stochastic process is a random function.
In practical applications, the domain over which the function is defined is a time interval (time series) or a region of space (random field).