ABSTRACT
Reliability is the science of predicting, estimating, or optimizing the life distribution of components or systems. The reliability of a product is a vital part of quality as perceived by the customer. The reliability of a system is characterized by the individual component reliabilities and by the contributions which individual components make to the reliability of the system. To improve system reliability, individual component reliabilities may be improved, or the system redesigned to make the contributions of individual components less critical. Failures which occur in some continuous medium, such as time, are said to occur as a Poisson process if the probability of a failure occurring at any time is constant and failures are independent. This is the notion of failures occurring 'at random'. The Weibull distribution arises as an asymptotic extreme value distribution. The Gumbel distribution has no shape parameter because it has a fixed shape.
