ABSTRACT
A detailed study of the probabilistic relations between components and systems inevitably involves a higher level of mathematical sophistication. The main emphasis of this chapter is to describe the models, and to give an outline of the mathematical derivation, with references for the reader desiring the full mathematical details. The best known class of reliability models is that of coherent systems. The fundamental concept of a coherent system is that the individual components are in one of two states, functioning or failed, and the state of the system is represented in terms of the states of individual components through what is called the structure function. Some interesting statistical problems arise in connection with coherent systems. Point estimation is generally no problem, because the reliability of the system may be estimated by substituting the point estimates of reliabilities of individual components. However, there are much more subtle problems connected with interval estimates, both classical and Bayesian.
