Statistics for Maintenance Modelling: Proportional Hazards and Accelerated Life Models

# Introduction¤

It is frequently the case that time to failure is dependent on other random variables --- characteristics which are perhaps subject to natural variation, but they may also be under a certain amount of control. These explanatory variables, sometimes called covariates, influence the life-time directly, or model it through the reliability function, and thus through the hazard function. Click here to jump to The Hazard Function screen in the Continuous Lifetime Distributions 1 session if you need to recap. The covariates may be time-dependent and they may be influenced over time by the unit itself (e.g. level of corrosion), or may not be directly involved in the failure process (e.g. applied stress).

In this session we discuss the analysis of maintenance and reliability data using the proportional hazards and accelerated life models. The proportional hazards model has been briefly introduced in the previous session on Regression Modelling. These two models are also called regression models since the covariates are sometimes also called regression variables.

R(t) = 1 - F(t) =