Statistics for Maintenance Modelling: Repairable Systems

# ROCOF¤

Under the power-law assumption, the ROCOF, or intensity function, is defined by:

(t) = {E(N(t))} = A

Thus if:

- 0 < < 1, then the ROCOF decreases
- = 1, the ROCOF is constant
- > 1, then the ROCOF increases.

Ascher and Feingold (1984) coined the terms of "happy system" and "sad system" where the ROCOF is decreasing and increasing, respectively.

The existence of trend is therefore characterised by linear plots which have slopes significantly different from 1. An approximate measure of the possible departure from 1 can be gained via a confidence interval estimate of the slope.

The ROCOF should not be confused with the hazard function. The hazard describes the conditional probability of failure within t +t of a non-repairable component given survived to t. It is possible for each Xi to have an increasing hazard but for the system to have a constant ROCOF, or indeed any other combination of behaviours. A battery may have Weibull distribution life time with shape parameter greater than 2, implying an increasing hazard, but a system in which the battery is replaced on failure by a similar battery may display constant ROCOF.