After the end of everyday, a production plant's maintenance crews check on the machinery and grade each item's state of repair. A particular robot arm can be given five grades: Excellent, Good, Satisfactory, Watch, Failed. If the robot arm is tagged with a Failed grade, a crew will be sent the next day to repair it. There is about a 70% chance the crew will be successful in repairing the arm back to an Excellent condition. Otherwise, they have to try again the next day to fix it. The general wear and tear of operation causes at most a single level of deterioration a day and this grade decrease happens about 25% of the time. During the day, the operators can tinker with the arm and are able to increase (if possible) the repair grade level 10 of the time. The operators cannot improve a Failed arm Management wants to model the daily grade level of a robot arm

(a) State any assumptions you need to utilize a Discrete Time Markov Chain.
(b) What are the possible states of your DTMC?
(c) Give the TPM.
(d) Draw the TPD