The life of a certain type of device has an advertised...

The life of a certain type of device has an advertised failure rate of 0.01 per hour. The failure rate is constant and the exponential distribution applies.
(a) What is the mean time to failure?
(b) What is the probability that 200 hours will pass before a failure is observed?

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Exponential Distribution

A statistical distribution often used to model the time between events in a process where events occur continuously and independently at a constant rate. It is characterized by its memoryless property, meaning the probability of an event occurring in the future is independent of the past.

Failure Rate

The constant rate, typically denoted as lambda (?), at which a device or system fails. In reliability studies, this value is critical as it defines the process's constant risk of failure per unit time.

Mean Time to Failure (MTTF)

The expected time until a device fails, which, for an exponential distribution, is calculated as the reciprocal of the failure rate. MTTF is a crucial metric in reliability engineering, indicating the average lifespan of a device.

Reliability Function

A function that quantifies the probability that a system or component will continue to operate without failure for a given amount of time. For the exponential distribution, it is given by the formula R(t) = exp(-?t), representing the chance of surviving beyond time t.

Transcript

Please give Ace some feedback