A reliability engineer for an appliance manufacturer investigates failure times for the heating element within the company's toasters. The engineer wants to determine the time at which specific proportions of heating elements fail in order to set the warranty period. Heating element failure times follow a normal distribution, with a mean of 1000 hours and a standard deviation of 300 hours.
The engineer uses the inverse CDF to determine the time by which 5% of the heating elements fail, the times between which 95% of all heating elements fail, and the time at which only 5% of the heating elements continue to function.
This example uses the normal distribution. However, these steps are similar for any distribution that you select.