Note7 - Reliability - Theory - Revised
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Fundamental Safety Engineering and Risk Management Concepts, 2012/2013 by M. J. Baker and H. Tan CLASSICAL RELIABILITY THEORY 1 Introduction Classical reliability theory describes the probability of a system completing its expected function during an interval of time. It is the ba sis of reliability engineering, which is an area o f study focused on optimizing the reliability, or probability of successful functioning, of systems, such as airplanes, linear accelerators, and any o ther product. It developed apart from the mainstream of probability and statistics. It was originally a tool to help nineteenth cen tury maritime insurance and life insurance companies compute profitable rates to charge their customers. The failure of mechanical device s such as ships, trains, and cars, is similar in many way s to the life or death of biological organisms. Death or failure is ca lled an "event", and the goal for the classical reliability theory is to project or forecast the rate of even ts for a given population or the probability of an event for an individual. 2 Reliability function Assume that nominally identical components are p ut into service under conditions which are also nominally identical and that the random time to failure of each component is observed. Furthermore, assume that a probability distribution is fitted to the random time to failure data. Take ) (t F T to be the resulting distribution function and ) (t f T to be the corresponding density function. Then the reliability function, ) (t R T , is defined as t T P t T P t F t R T T 1 ) ( 1 ) ( (1) Hence, t T T d f t R 0 ) ( 1 ) ( (2) Eventually all components fail, so lim () 0 T t R t (3)
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