integration variable. Here can be thought of as the instantaneous failure rate, i.e. the probability of failure in the time interval between and , as tends towards :

Hazard rate

A concept closely related but different to instantaneous failure rate is the hazard rate (or '), . In the many-system case, this is defined as the proportional failure rate of the systems still functioning at time - as opposed to , which is the expressed as a proportion of the initial number of systems.

For convenience

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