Decision tree question

[malielin]

hi, I'm struggling with this decision tree question:

A part of an aircraft engine can be given a test before installation. The test has only a 75 % chance of revealing a defect if it is present, and the same chance of passing a sound (good) part. Whether or not the part has been tested it may undergo an expensive rework operation which is certain to produce a part free from defects. The cost of rework is £1000. If a defective part is installed in the engine the loss is £5000. Suppose 1 in 8 of parts are initially defective, and the cost of the test is £C.
(a) Draw the decision tree, evaluate all probabilities and determine, in terms of C, all the optimal decisions.
(b) How much should the manager be willing to pay for the test?

I know it's probably a simple question, and I understand the basics, but I'm having trouble processing the wording, and what I have so far doesn't feel like it's the right answer. I have attached what I have done so far(sorry it's messy, as it was rough work), if someone could give me some help as where I have gone wrong that would be great.
Thank you.

 

[Romsek]

You don't say what happens if the test reveals a defective part. Is that part discarded, and another selected? Does the entire assembly process just halt? What are the associated costs?

 

[malielin]

You don't say what happens if the test reveals a defective part. Is that part discarded, and another selected? Does the entire assembly process just halt? What are the associated costs?

That is the whole question, that’s all I have to work with. So, your guess is as good as mine.
I assume the test is mean tot just say what the part is(good/defective) and then the decision is up to the manager.

 

[Romsek]

I'm going to look at it like this.

We get a part. We test it. If it passes, we use it. If not we rework it and use it.

That vs. no testing and we just use all parts we get.

Sound ok?

 

[firemath]

I have attached what I have done so far(sorry it's messy, as it was rough work)......

On the contrary, your decision trees are quite nice!

 

[Romsek]

Here's the setup as I see it. See if you agree with this.




and of course the no test situation is



The idea is to come up with the test cost c that equates the expected overall cost of the process. If the test then costs less than c you are saving money on average. It should be pretty obvious that the expected cost of the process for the no test situation is

\(\displaystyle E[C_{total}] = \dfrac 1 8 \cdot 5000 = 625\)