Reliability Theory

a scientific discipline that develops and studies methods of ensuring the operational efficiency of products, equipment, systems, and the like. Reliability theory involves (1) the use of reliability indexes, (2) the justification of requirements for reliability taking into account economic and other factors, and (3) the development of recommendations for ensuring specified requirements for reliability at the stages of design, production, storage, and operation.

Quantitative reliability indexes are introduced into reliability theory by the construction of mathematical models of the given objects. Different mathematical methods are used in reliability theory; particularly useful are the methods of probability theory and mathematical statistics because the events that describe the reliability indexes, such as the instant of failure or the duration of maintenance, are often random. Analytical methods from the theory of random processes are used to calculate the probability of failure-free operation over a given period. The calculation of quantitative reliability indexes taking into account the feasibility of repairing equipment that has failed is in many ways similar to the design of systems in queuing theory. Analytical methods for calculating reliability are combined with computer simulation methods.