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# Advanced Computational Techniques in Engineering

ENGG7302 Advanced Computational Techniques in Engineering Lecturer: Hanna Kurniawati Assignment 2 – Stochastic Processes Applications Due: Friday, 1 June 2018 13:00. Submission: Codes and a .pdf file of the answers in a single .zip file through turnitin. Reminder: NO cheating!!! UQ-Maintenance is developing a Machine Health Monitoring System to help in maintaining the many machines in various parts of UQ. For efficiency, the machines’ maintenance record are kept at the school level. For resource allocation purposes, UQ-Maintenance models the arrival of new machines in each school as independent Bernoulli Process, though they may not be identical. UQ models the health of a machine as a Markov Chain, where the states represent the health levels of the machines at the end of each month and a single transition step represents the changes in the machine’s health over the duration of one month. The transition from one state to another is modeled as independent Binomial disDocument Preview:

The University of Queensland ENGG7302 Advanced Computational Techniques in Engineering Lecturer: Hanna Kurniawati Assignment 2 – Stochastic Processes Applications Due: Friday, 1 June 2018 13:00. Submission: Codes and a .pdf ?le of the answers in a single .zip ?le through turnitin. Reminder: NO cheating!!! UQ-Maintenance is developing a Machine Health Monitoring System to help in maintain- ing the many machines in various parts of UQ. For ef?ciency, the machines’ maintenance record are kept at the school level. For resource allocation purposes, UQ-Maintenance models the arrival of new machines in each school as independent Bernoulli Process, though they may not be identical. UQ models the health of a machine as a Markov Chain, where the states represent the health levels of the machines at the end of each month and a single transition step represents the changes in the machine’s health over the duration of one month. The transition from one state to another is modeled as independent Binomial distributions. This means, assuming X is the random variable that represents the state of the Markov Chain at time-step i, i P(X jX =s) is a Binomial distribution, for any states in the state space of the Markov t+1 t Chain ; the binomial distribution for different values ofX are independent, but they might t have different parameters. Of course, different types of machines may be modelled as different Markov Chain. How- ever, each Markov Chain will have one state that represents “break down and must be repaired” and one state that represents “pristine condition”. Furthermore, for simplicity, UQ-Maintenance models all machines in the same school with the same Markov Chain. Your tasks are: [40 points] I: Programming Please write a Matlab program (.m ?le) with 2 outputs: A single vector, where each element is the average number of machines at each of UQ school that are in state “break down and must be repaired” at the end of month-1, month-2, … , month-12, assuming at the…