Conceiving reliablesystems is a strategic issue for any industrial society. Hence, reliability has become a discipline at the beginning of the Second World War. In fact, reliability is a field of reseach common to mathematics, operational research, informatics, graph theory, physics, and so forth. We are concerned here with the mathematical side of reliability, of which probability, statistics, and more specially stochastic processes theory constitute the natural basis. US army during the war, and later in the US Problems encountered by the and Soviet space programs, have led to an awarenessofthe need for reliabilityor more generaly for dependability (a general term covering reliability, availability, security, maintainability, etc.) of the systems. The paper by W. Weibull of 1938 on the strength of materials, leading to the distribution that later took his name, and the paper by B. Epstein and M. Sobel of 1951, initiating the use of the exponential distribution as the basic (and now most used) model for reliability, are the founding papers of the field. At this time, the systems were merely seen as black boxes. During the 1960s, they began to be considered as the result of the interaction of their elements. Appropriate methods were then developed, from Shannon's work to the beautiful theory of coherent systems initiated by Z.W. Birnbaum, J.D.