A company uses three different assembly lines- A1, A2, and A3- to manufacture a

Question

A company uses three different assembly lines- A1, A2, and A3- to manufacture a particular component. Of thosemanufactured by line A1, 5% need rework to remedy a defect, whereas8% of A2's components need rework and 10% of A3's need rework.Suppose that 50% of all components are produced by Line A1, 30% areproduced by line A2, and 20% come from line A3. Construct a tree diagram with first-generation branches corresponding to the three lines. Leading from each branch, draw one branch for rework (R) and another for no rework (N). Then enter appropriate probabilities on the branches.

Explanation / Answer

let n=1,2,3

An is the event that randomly selected component with manufactured by line An.

Let R be the event the component needs rework

so P(A1)=0.5,

P(A2)=0.3,

P(A3)=0.2

also P(R|A1)=0.05,

P(R|A2)=0.08,

P(R|A3)=0.1,

for find most likely line we use Bayes theorem

P(An|R)=P(An)*P(R|An))/P(R)

for comparing P(An|R) the numerator is given by

for n=1,P(An)P(R|An)=0.025
n=2,P(An)P(R|An)=0.024
n=3,P(An)P(R|An)=0.02

Means A1 is most likely while A3 is least likely.

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