An article published in the annual Journal of Industrial Engineering (2013) studied preventive maintenance operations for fuel dispensers in a chain of gas stations. The time between failures of fuel dispensers at high failure stations was assumed to have an exponential distribution with a mean of 460 hours. Also, the time between preventive maintenance activities for the fuel dispensers has an exponential distribution with mean 2,880 hours.

a. Find and interpret the hazard rate for the failure time distribution.

b. Find and interpret the hazard rate for the preventive maintenance time distribution.

c. Assuming the failure time and preventive maintenance time distributions are independent, the research showed that the time between maintenance activities (either preventive maintenance or corrective maintenance due to failures) has an exponential distribution with mean 395 hours. Find and interpret the hazard rate for the time between any maintenance activity (either preventive or corrective).