Statistics for Maintenance Modelling: Continuous Lifetime Distributions 1

# Explaining the Hazard Function¤

To see why we need to divide through by the survivor function consider the probability of throwing 6 consecutive heads with an unbiased coin. The probability of achieving this on each attempt is (½)6 = 1/64.

However if our current attempt has just successfully thrown a 4th consecutive head, then the probability of making it to 6 consecutive heads is just the probability of throwing 2 more heads i.e. (½)2 . This is given by the original probability (½)6 divided through by the probability of surviving so far (i.e. of having thrown 4 heads) of (½)4.

In a similar way the probability of someone who has just had their 100th birthday dying in the next year are quite high, but the probability of them dying between their 100th and 101st birthdays when they were born was very low.

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