The hazard function provides a measure of the likelihood of failure as a function of how long a unit has survived (the instantaneous failure rate at a particular time, t).

Although the nonparametric hazard function is not dependent on any specific distribution, you can use it to help determine which distribution might be appropriate for modeling the data if you decide to use parametric estimation methods. Select a distribution that has a hazard function that resembles the nonparametric hazard function.

For the new muffler data, the likelihood of failure is 10.36 (0.0000114/0.0000011) times greater for the new type of mufflers at 55,000 miles than it is at 35,000 miles.

The density estimates describe the distribution of failure times and provide a measure of the likelihood that a product fails at particular times.

Although the nonparametric density function is not dependent on any specific distribution, you can use it to help determine which distribution might be appropriate for modeling the data if you decide to use a parametric estimation methods. Select a distribution that has a density function that resembles the nonparametric density function.

For the new muffler data, the likelihood of failure is 10.3 (0.0000103/0.0000010) times greater for the new type of mufflers at 55,000 miles than it is at 35,000 miles.