The term "Failure time" is used to show the length of time from a certain starting point (Usually the starting point of the observation) until the death of life or failure of a product.
The term Failure time is widely applied in Life insurance, reliability study, medical research, and clinical trials.
It is now used in a wide range of useful applications in the finance and insurance industries, referred to as showing any time duration until a certain event of interest occurred. For example,
the time until the company becomes insolvent,
the time until the next tsunami strikes,
the time until an insured person makes the first health insurance or motor claim,
the time until a stock hits a striking price
In Life Insurance and mortality studies, the failure time is usually called a lifetime.