A brake component has been in use for one year. During that time, 125 incidents have been recorded over an estimated 4,120,000 miles. It is assumed that the time to failure is distributed exponentially.

The Relyable trucking Company operates two trucks. The brake component outlined in above mentioned situation has been installed on each wheel subsystem (4 on each truck). Over the next year, they expect to accumulate 12,360 miles on each truck. They have two spare brake components in their inventory and will immediately replace the brake component in the event of a failure. What is the one-year reliability of the fleet of two trucks, solely with respect to this brake component, if a fleet failure occurs when the third failure occurs?

Reminder: If a component that has a constant failure rate is immediately repaired or replaced, then the number of failures observed over some time, t, has a discrete Poisson distribution.