Refer back to given Problem. Power Tech has decided to use the XI000 model exclusively for producing plastic moulded covers. The revenue for each non-defective unit is SO. 10. For the defective units, rework costs are SO. 15 per unit.
(a) Show the analytical expression for the total revenue.
(b) Using the same probability distribution as in given Problem, create a table showing the random number assignment ranges for the number of defective units.
(c) Assume that the X1000 model produces moulded covers in batches of 100. Carry out a Monte Carlo simulation of 100 production runs.
What is the average total revenue? What are the maximum and minimum revenue in the 100 trials? Construct a histogram of the total revenue and comment on your results.
Problem :
Power Tech builds power-surge protection devices. One of the components, a plastic moulded cover, can be produced by two automated machines, Al and X1000. Each machine produces a number of defects with probabilities shown in the following table.
|
AI
|
X1000
|
|
No. of defects(out of 100)
|
Probability
|
No. of Defects (out of 100)
|
Probability
|
|
0
|
0.3
|
0
|
0.25
|
|
1
|
0.28
|
1
|
0.33
|
|
2
|
0.15
|
2
|
0.26
|
|
3
|
0.15
|
3
|
0.1
|
|
4
|
0.1
|
4
|
0.05
|
|
5
|
0.02
|
5
|
0.01
|
(a) Which machine is better with regard to the expected number of defective products?
(b) If Power Tech wants to take the variance of the number of defects into account, can mean-variance dominance be used to select a preferable machine?