Develop a report addressing the specific exercises set out in the guideline below. Your report should be 2000-2500 words, excluding
Title, Abstract, Table of contents, Bibliography and Appendices.
Exercise 1. (50%)
An important part of a production line has to be repaired. The industrial company is impacted by the stop of the production. Each day without producing costs
the company $64 000. The maintenance team has only three possible options:
Option 1
He can return the part to the supplier who has agreed to collect, repair, and return it for free. However, there is no compensation for any losses supported by the
company because the machine is not working. The supplier will not agree to repair the machine if there has been a previous attempt to repair it. If the machine is
returned, the supplier will guarantee to return it in working order in 5 days’ time.
Option 2
He can call in a repairing company. They will charge $40 000 to carry out the repair and they estimate that there is a 20% chance that they will be able to return
the machine to working order in 2 days. There is, however, a 80% chance that repairs will take 4 days.
Option 3
The maintenance team can attempt to repair it. He estimates that there is a 40% chance that he could mend the machine in 4 days. However, if at the end of 4
days the attempted repair has not been successful, he will have to decide whether to call the repairing company or to make a second attempt to repair. This would
take 3 further days, and he estimates that there is a 35% chance that this second attempt would be successful. If he fails at the second attempt, he will have no
alternative other than to call in the repairing company.
(a) Draw the decision tree of this problem
(b) Assuming that the maintenance department wants is to minimize the expected costs, what policy should they follow?
Exercise 2. (50%)
The company ABC is one of the most important specialists in electronic products.
In the last weeks there are several customers’ complaints due to the poor quality.
One of the Operations Managers starts a Quality Control to detect the possible problems.
After one week, the most common defects and their frequency are in the following table:
Defects DAYS
1 2 3 4 5 6 7
1 Too long 65 50 12 24 55 23 28
2 Bad quality material 21 32 14 11 20 18 10
3 Wrong labelling 3 3 1 2 0 4 5
4 Broken 0 3 0 3 0 3 0
5 Wrong date 20 16 15 20 18 16 18
6 Wrong packaging 0 8 0 4 3 4 5
7 Lack of components 17 11 12 10 17 19 24
8 Too short 1 0 4 0 4 2 3
9 Excess of components 69 57 58 55 62 59 65
10 Wrong components 5 1 7 2 4 6 1
TOTAL DEFECTS
(a) Draw the control chart that shows the evolution of the rate U= defects/unit (in %) in one week. If the same number of units are checked every day and
the goal is 1.5%, are we achieving the expectations?
(b) Construct the Pareto Chart and sort the defects in three groups according to the frequency.
One of the most common problems is related to the length of the product. A sample of 50 units (10 groups of 5 elements) is taken.
If the specification is 10+0.5, do you think that the process is making parts longer than usual?
1 2 3 4 5 6 7 8 9 10
10 10.1 10.2 10.2 10 10.3 10.2 10.1 10 10.3
10.2 10.3 9.9 9.8 10.1 10.2 10 10.1 9.9 10.1
10.3 10 10.1 10 10.2 10.1 10.1 10 10.3 10
9.8 9.9 10.3 10.1 10 10.4 9.8 10.1 10.1 10.2
10.1 10.2 10.4 10 9.9 9.7 10 9.8 10.4 9.9
(c) Compute the average of data, draw the control chart of the 10 groups and the histogram of 50 units to justify your answer.
Checking for possible causes that explain the problem, the manager concludes that the machinery is old, and the maintenance is poor.
(d) Suggest an Action Plan with several solutions to fix the problem.
