Statistics for Maintenance Modelling: Continuous Lifetime Distributions 1

# The Hazard Function¤

Following on from this, the rate at which items fail at the end of year 2 (start of year 3) is: . Generalising this gives the (conditional) failure rate function or the hazard function:

The hazard function expresses the propensity for a part to fail shortly after time t given that it has survived to time t, i.e. the probability of failing in the time interval (t, t+ t) assuming that the part has lasted until time t, is approximately t h(t).

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## The Exponential Form of the Reliability (Survival) Function

Since from the previous screen, , we have . Solving this differential equation gives us:

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