8. Assessing Product Reliability
8.1. Introduction
8.1.2. What are the basic terms and models used for reliability evaluation?

## Repair rate or ROCOF

Repair Rate models are based on counting the cumulative number of failures over time A different approach is used for modeling the rate of occurrence of failure incidences for a repairable system. In this chapter, these rates are called repair rates (not to be confused with the length of time for a repair, which is not discussed in this chapter). Time is measured by system power-on-hours from initial turn-on at time zero, to the end of system life. Failures occur as given system ages and the system is repaired to a state that may be the same as new, or better, or worse. The frequency of repairs may be increasing, decreasing, or staying at a roughly constant rate.

Let $$N(t)$$ be a counting function that keeps track of the cumulative number of failures a given system has had from time zero to time $$t$$. $$N(t)$$ is a step function that jumps up one every time a failure occurs and stays at the new level until the next failure.

Every system will have its own observed $$N(t)$$ function over time. If we observed the $$N(t)$$ curves for a large number of similar systems and "averaged" these curves, we would have an estimate of $$M(t)$$ = the expected number (average number) of cumulative failures by time $$t$$ for these systems.

The Repair Rate (or ROCOF) is the mean rate of failures per unit time The derivative of $$M(t)$$, denoted $$m(t)$$, is defined to be the Repair Rate or the Rate Of Occurrence Of Failures at Time $$t$$, or ROCOF.

Models for $$N(t)$$, $$M(t)$$, and $$m(t)$$ will be described in the section on Repair Rate Models.