Statistics for Maintenance Modelling: Proportional Hazards and Accelerated Life Models

# Nonparametric Estimation of the Survival and Hazard Functions¤

Alternatively, it is possible to obtain a nonparametric estimate of h0(t) once = (1, 2, ... n) have been estimated. The next formula is a generalisation of the Kaplan-Meier (see the Nonparametric Estimates of the Survival Function screen in the Model Selection session) estimator described in the Preliminary Model Selection session:

where = the item hasn't failed at time t(j) given failure times t(1), ..., t(r).

A plot of the empirical survival function 0(t) may suggest a suitable parametric form for 0(t) and an estimate of the baseline cumulative hazard function is 0(t) = -ln 0(t).