Abstract
Risk analysis requires estimation of hazard functions. A hazard rate is the conditional probability of adverse sentinel event occurring in the next time period, given that it has not yet occurred. This tutorial shows how hazard functions are estimated from survival functions, the probability of going through a time period without the sentinel event. Survival functions are built on cumulative distribution functions, which measure the probability of occurrence of sentinel event in current and prior time periods. Cumulative distribution functions are calculated from probability density functions, which give the probability of an event occurring at a particular time period. Probability density functions are typically estimated from incidence reports, which are readily available to safety officers. Sometimes, these functions are estimated by making assumptions about the shape of the distribution function. For discrete data, the typical probability density functions are Bernoulli, Binominal, Geometric, and Poisson distributions. This tutorial starts with estimating a probability distribution and then proceeds to calculation of hazard and relative risk rates.