If a non-repairable component has a constant hazard rate, the time to failure follows which distribution?

• A. Normal
• B. Uniform
• C. Lognormal
• D. Exponential

Answer: (D)

When the hazard rate is constant, the chance of failing in the next instant does not depend on how long the component has already been in operation. That leads to the exponential distribution for the time-to-failure. Mathematically, if the hazard rate is h, the survival function is S(t) = e^{-h t} and the failure density is f(t) = h e^{-h t}. This is the exponential distribution with rate h. A key consequence is the memoryless property: surviving up to a time s gives no information about the probability of surviving beyond s+t, beyond what is already known from t. This memoryless behavior is a hallmark of the exponential model and fits a non-repairable component where the risk of failure is the same at any age.

Other distributions don’t match a constant hazard. The normal distribution allows negative lifetimes and has a hazard that changes with time. The uniform distribution implies a fixed window of possible lifetimes, which doesn’t reflect a constant failure risk over all time. The lognormal models lifetimes influenced by multiplicative factors and typically shows increasing hazard over time. Therefore, the exponential distribution is the appropriate model for a constant hazard rate.