Statistics for Maintenance Modelling: Regression Modelling

# Accelerated Life Models¤

Accelerated life models make use of the survival function (see The Reliability Function screen in the Continuous Lifetime Distributions 1 session). The premise is that the rate to failure of a component is 'accelerated' by some multiplier, the multiplier being a function of the covariate, for example the load. Formally, the accelerated life model holds when:

S(t;x) = P{T t|x}

In other words, the survival function of t and x is equal to the probability of the time to failure being greater than t given the value of x, where x is the covariate, say load again.

S(t;x) = S0(tx) where S0 is some baseline survival function and x is a positive function of x.

## Example

Let T denote the time to breakdown of an electrical component subjected to constant voltage x, and suppose x = for some > 0 and S0(t) = . Then, S(t;x) = , so T is exponentially distributed with mean (since from R(t) = ,
= -1, and is the mean. See The Weibull Distribution and The Reliability Function for the Weibull Distribution screens in the Continuous Lifetime Distributions 1 session).

Note that 0 = 0 here.

The choice of baseline function is made by the modeller, but experience can be used to make more appropriate decisions.