what is the hazard rate 
the hazard rate refers to the rate of death for an item of a given age x it is part of a larger equation called the hazard function which analyzes the likelihood that an item will survive to a certain point in time based on its survival to an earlier time t in other words it is the likelihood that if something survives to one moment it will also survive to the next the hazard rate only applies to items that cannot be repaired and is sometimes referred to as the failure rate it is fundamental to the design of safe systems in applications and is often relied on in commerce engineering finance insurance and regulatory industries understanding the hazard ratethe hazard rate measures the propensity of an item to fail or die depending on the age it has reached it is part of a wider branch of statistics called survival analysis which is a set of methods for predicting the amount of time until a certain event occurs such as the death or failure of an engineering system or component the concept is applied to other branches of research under slightly different names including reliability analysis engineering duration analysis economics and event history analysis sociology calculating the hazard ratethe hazard rate for any time can be determined using the following equation h t f t r t h t f t r t h t f t r t f t is the probability density function pdf or the probability that the value failure or death will fall in a specified interval such as a specific year r t on the other hand represents the survival function or the probability that something will survive past a certain time t the hazard rate cannot be negative and it is necessary to have a set lifetime on which to model the equation example of the hazard ratethe probability density calculates the probability of failure at any given time for instance a person is certain to die eventually as you get older you have a greater chance of dying at a specific age since the average failure rate is calculated as a fraction of the number of units that exist in a specific interval divided by the number of total units at the beginning of the interval if we were to calculate a person s chances of dying at a certain age we would divide one year by the number of years that person potentially has left to live this number would grow larger each year a person aged 60 would have a higher probability of dying at age 65 than a person aged 30 because the person aged 30 still has many more units of time years left in their life and the probability that the person will die during one specific unit of time is lower the shape of the hazard rate curvein many instances the hazard rate can resemble the shape of a bathtub 1 the curve slopes downwards at the beginning indicating a decreasing hazard rate then levels out to be constant before moving upwards as the item in question ages think of it this way when an auto manufacturer puts together a car its components are not expected to fail in its first few years of service however as the car ages the probability of malfunction increases by the time the curve slopes upwards the useful life period of the product has expired and the chance of non random issues suddenly occurring becomes much more likely 