The exponential distribution can be written as
Beta is called the scale parameter and lambda the rate parameter.
5-8 hour shifts is 40 hours. The probability it does not break down in this
time can then be found by integrating over 0 to 40 and subtracting from 1
Or, if the machine does not break down within 40 hours, then it is sure to breakdown some time after that. Whenever that may be.