# Certainty, reliability

A priori conviction of the realization of some event, to the exclusion of any doubt. Certainty is a characterization of the realizability of some event, and is labelled with the highest degree of probability. In probability theory the concept of certainty is connected with certain events (cf. Certain event) and with events occurring with probability one. In practice, one speaks of certainty even when the probability of some event is sufficiently close to one.

#### Comments

Reliability theory is the theory studying the probability of correct functioning of a manufactured system. The reliability of such a system is its probability of functioning correctly (and, hence, the reliability is $\leq1$, in general). The reliability function is the same probability as a function of time and/or other parameters involved in the system. There is, e.g., the reliability function of a communication channel, cf. Erroneous decoding, probability of.

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Certainty, reliability.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Certainty,_reliability&oldid=32969