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1.Let X denote the processing time for a particular drilling operation. There ar

ID: 3011634 • Letter: 1

Question

1.Let X denote the processing time for a particular drilling operation. There are three types of parts: A, B, and C. Thirty percent of type A, sixty five percent of type B, and five percent of type C. Drill time for a type A is exponential with mean 3.2 minutes. Drill time for a type B is uniformly distributed between 1.2 and 2.0 minutes. Drill time for a type C part is deterministically 0.5 minutes. Parts arrive randomly and independently to the drill.

a) Develop a model for the processing time

b) Use simulation to find the expected processing time.

c) Report a 95% confidence interval for mean processing time

Explanation / Answer

Let Y be the overall drill time, YA be type A drill time, YB for B and YC for C.

Then FY(y) = 0.30*FYA(y) + 0.65*FYB(y) + 0.05*FYC(y),

where,

FYA (y) = 1 exp(y/3.2) for y 0 and "0" otherwise,

FYB(y) = (y 1.2) / (2 1.2) for 1.2 y 2, "0" if y 1.2 and "1" otherwise,

And FYC (y) = 1 if y 0.5 and "0" otherwise.

Produce u from U (0,1).

If u < 0.3, set S = A ;

elseif u < 0.95, set S = B ;

else set S = C.

Produce u independently from U (0, 1).

Return y = FYS1 (u).