Statistical Models for Survival and Reliability Analyses

Abstract

Survival analysis and reliability analysis are the fields of statistics that deal with data related to the time to a specific event for an individual, such as the patient's survival time or the failure time of devices. This paper reviews the historical background and statistical properties of failure time models used in survival and reliability analyses. The paper is a tutorial, tailored for beginners. Basic survival analysis tools and concepts such as survival time, survival functions and hazard functions are defined, and their statistical properties and interpretations are explained. The general parametric models, such as the exponential, Weibull, and lognormal distributions, as well as regression models, such as the Cox proportional hazard model and accelerated failure time model, are also explained. Competing risk models are also briefly discussed. The data used in this paper, the derivation of the equations, and the R code for the data analysis are given in Appendix.