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
Consider the the same production plan as in Problem 1. Management has now assigned a score to each grade level: 4 - Excellent; 3 - Good; 2 - Satisfactory; 1 Watch; 0 Failed. They are interested to know how the score changes throughout a 7-day cycle.
(a) What is probability that an arm with a score of 4 will have a score of 4 after 7 days?
(b) Repeat (a) for all possible ending scores after 7 days (starting score remains 4).
(c) Using (b), what is the expected score of a robot arm after 7 days if it began n excellent condition.