A constant failure rate would have what type of histogram/distribution?

A constant failure rate indicates that the likelihood of failure remains the same over time, which is characteristic of an exponential distribution. This distribution is specifically used in reliability engineering to model the time until an event occurs, particularly in scenarios where the failure rate is constant. In an exponential distribution histogram, as time progresses, the number of failures occurring remains consistent, resulting in a specific shape that reflects this constant failure rate.

The exponential distribution is defined by its memoryless property, meaning the probability of failure at a certain time does not depend on how much time has already passed. This is a critical characteristic in reliability assessments, as it allows engineers to predict failure behaviors accurately over time based on historical data.

In comparison, the other options represent different types of distributions that do not align with the concept of a constant failure rate. For instance, a normal distribution has a bell-shaped curve, indicating variations and is applicable for data that clusters around a mean value. Log-normal distributions apply to scenarios where the logarithm of the data follows a normal distribution, typically appropriate for multiplicative processes. A uniform distribution indicates a constant probability across all values, rather than a rate applicable to failure over time. Thus, only the exponential distribution correctly represents a constant failure rate scenario.