Statistics for Maintenance Modelling: Continuous Lifetime Distributions 1

# The Reliability Function¤

As we saw in the previous session, the cumulative density function (cdf) - which gives the probability that an item fails before time t - is given by:

F(t) = P(T t) = .

It follows that:

.

The probability that the item survives beyond time t is one minus the cdf. This is called the reliability function (also known as the survival function) and is denoted by R(t) (or S(t)). Hence:

R(t) = 1 - F(t) = .

It follows that:

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