Suppose you buy an electronic device that you operate continuously. The device costs you $100 and carries a 1-year warranty. The warranty states that if the device fails during its first year of use, you get a new device for no cost, and this new device carries exactly the same warranty. However, if it fails after the first year of use, the warranty is of no value. You need this device for the next 6 years. Therefore, any time the device fails outside its warranty period, you must pay $100 for another device of the same kind. (We assume the price does not increase during the 6-year period.) The time until failure for a device is gamma distributed with parameters α = 2 and β = 0.5. (This implies a mean of 1 year.) Use simulation to simulate the 6-year period and include the following as outputs.
a. What is your total cost?
b. What is the number of failures during the warranty period?
c. What is the number of devices owned during the six-year period?