Methods for displaying and calibration of Cox proportional hazards models

Cox proportional hazards modelling is a widely used technique for determining relationships between observed data and the risk of asset failure when model performance is satisfactory. Cox proportional hazards models possess good explanatory power and are used by asset managers to gain insight into factors influencing asset life. However, validation of Cox proportional hazards models is not straightforward and is seldom considered in the maintenance literature. A comprehensive validation process is a necessary foundation to build trust in the failure models that underpin remaining useful life prediction. This article describes data splitting, model discrimination, misspecification and fit methods necessary to build trust in the ability of a Cox proportional hazards model to predict failures on out-of-sample assets. Specifically, we consider (1) Prognostic Index comparison for training and test sets, (2) Kaplan-Meier curves for different risk bands, (3) hazard ratios across different risk bands and (4) calibration of predictions using cross-validation. A Cox proportional hazards model on an industry data set of water pipe assets is used for illustrative purposes. Furthermore, because we are dealing with a non-statistical managerial audience, we demonstrate how graphical techniques, such as forest plots and nomograms, can be used to present prediction results in an easy to interpret way.