You are managing a lab which tests prototypes for compliance with safety regulat

Question

You are managing a lab which tests prototypes for compliance with safety regulations. A project manager has given you two prototypes to test, A and B, for his project, with the goal to identify at least that meets the safety regulations.

You calculate that prototype A has 30% likelihood of meeting the regulations and B has 40% chance of meeting the regulations. The profits (value) if we meet the regulations using any prototype is $100, and the value if we do not meet the regulation is $0. Suppose the cost of testing each prototype is $20. [Note that we only want to identify one prototype, and there is no additional value in identifying two prototypes that comply with regulations]

If we could test only one prototype, which prototype would we test? What is the expected value of following this strategy (of testing only one prototype)?

Suppose we decide to test both prototypes simultaneously, and then choose the prototype that complies with the safety regulation. What is the expected value of following this strategy?

Suppose we build in enough flexibility in our resource scheduling and follow the following sequential strategy: we can test one prototype and then continue onto test the next one only if the first one didn’t meet the regulations. What is the value of following this sequential strategy if

(a)     We test A first. And if A doesn’t meet the guidelines, we test B

(b)     We test B first, and if B doesn’t meet the guidelines, we test A.

[Note that to undertake this sequential strategy we need to be able to tentatively schedule resources for the second test, with the understanding that there is a non-zero chance that the resource would not be utilized and hence would have to re-allocated. Hence the strategy requires flexibility in resource scheduling]

Any help is greatly appreciated!! :)

Explanation / Answer

1. If we could test only one prototype then we will test prototype B as it has highest probability to meet the guidelines i.e 40%

Probability of B meeting requirements = 0.40

Profit if the prototype meet regulation = $100

Expected Value of testing Prototype = (0.4 * 100) - $20 = $20

2. Expected Value of testing both Prototypes = (0.4 * 100) + (0.3 * 100) - $40 = $30

3.

a. We test A first. And if A doesn’t meet the guidelines, we test B

Expected Value = A fails + B pass = $0 + (0.4*100) - $40 = $0

b. We test B first, and if B doesn’t meet the guidelines, we test A

Expected Value = B fails + A pass = $0 + (0.3*100) - $40 = -$10

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