Abstract
Abstract The hazard function is a tool for describing the process of time to failure. Hazard functions arise in the context of survival analysis, also known as failure analysis , and provide a convenient way to visualize how the risk of failure changes with age or time. The exponential, Weibull, and lognormal distribution are three of the commonly used statistical models of time to failure. Hazard functions are used in epidemiology, medicine, ecology, engineering, and manufacturing settings, as well as in economics and finance. In this article, the mathematical concept of hazard and typical survival or failure time models are discussed. The hazard ratio is a general way of examining relative risk. Cox proportional hazard models are examined, and nonparametric statistical methods for describing the relative risk of failure for two or more populations are discussed.
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