Reliability Function

Sampling

Probability Density Function

Cumulative Distribution Function

Hazard Function

Expectation

Exam

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The reliability function is the complement of the cumulative distribution function.  If modeling the time to fail, the cumulative distribution function represents the probability of failure and the reliability function represents the probability of survival. Thus, the cumulative distribution function increases from zero to one as the value of x increases, and the reliability function decreases from one to zero as the value of x increases. This is shown in the figure below.

As seen from the figure above the probability that the time to fail is greater than 190 is 0.7475 which is the reliability at time = 190.  The probability that the time to fail is less than 190, the cumulative distribution function, is 1 - 0.7475 = 0.2525. Mathematically, the reliability function is the integral of the probability density function from x to infinity.