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 ve 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 60% 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 x 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. Required:
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