Statistics for Maintenance Modelling: Proportional Hazards and Accelerated Life Models

# The Proportional Hazards Model¤

The proportional hazards model was first proposed by Cox (1972). The vast majority of reported uses of the proportional hazards model have been in the areas of survival analysis of medical data. It is noted that however, the proportional hazards model has been increasingly used in reliability and maintenance modelling research.

The proportional hazards (PH) model introduced in the previous session on Regression Modelling, models the effects on the hazard function of certain explanatory covariates or factors associated with the life-time of equipment. The PH model assumes that, under conditions given by a vector y = (y1, y2, ... , yn) of covariates, the hazard function is of the form:

h(t;y) = h0(t) g(y)

where h0(t) is the baseline hazard function and g(y) is some function of y. Thus the combined effect of y is simply to scale the hazard function up or down. Since:

is independent of t, the hazards at different y values are in constant proportion over time. The function g(y) may take a variety of forms and the most commonly used one is which is the form that shall be used in this session where = (1, 2, ... n).