When reliability is expressed as a function of time, the continuous random variable, not negative, of interest is T, the instant of failure of the device. Let f(t) be the probability density function of T, and let F(t) be the cumulative distribution function of T. F(t) is also known as failure function or unreliability function1.
In the context of reliability, two additional functions are often used: the reliability and the hazard function. Let’s define Reliability R(t) as the survival function:
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The Mean Time To Failure - MTTF is defined as the expected value of the failure time:
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Integrating by parts, we can prove the equivalent expression:
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