Let X denote the processing tune for a particular drilling operation. There are
ID: 3011725 • Letter: L
Question
Let X denote the processing tune for a particular drilling operation. There are three types of parts: B, and Thirty percent of type A, sixty five percent of type and five percent of type Drill tune 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. Dull time for a type C part is deterministically 0.5 minutes. Parts arrive randomly and independently to the drill. Develop a model for the processing tune. Use simulation to find the expected processing time. Report a 95% confidence interval for mean processing time. (Box-Muller Method) If U_1 and U_2 are independent Uniform(0, 1) and X_1 = squareroot of -2In(U_1) cos(2pi U_2) and X_2 = squareroot of -21N(U_1) sin (2 pi U_2) Use simulation to generate pairs of X_1 and X_2. Plot histograms for X_1 and X_2. Do they look like normal distributions? Report means and standard deviations for X_1 and X_2. Report covariance of X_1 and X_2. Are they independent? Why? Use simulated data of X_1 to calculate P(X_1 less than or equal to 1.96). Develop a simulation for the following problem. The management of Madeira Manufacturing Company is considering the introduction of a new product. The fixed cost to begin the production of the product is dollar 30,000. The variable cost for the product is uniformly distributed between dollar 16 and dollar 24 per unit. The product will sell for dollar 50 per unit. Demand for the product is best described by a normal probability distribution with a mean of 1200 units and a standard deviation of 300 units. Use simulation trials to answer the following questions: What is the mean profit for the simulation? What is the probability that the project will result in a loss? What is your recommendation concerning the introduction of the product?Explanation / Answer
1. Consider Z be the overall drill time, ZA be type A drill time, ZB for B and ZC for C.
=> FZ(z) = 0.30*FZA(z) + 0.65*FZB(z) + 0.05*FZC(z),
where,
FZA (z) = 1 exp(z/3.2) for z 0 and 0 else,
FZB(z) = (z 1.2) / (2 1.2) for 1.2 z 2, 0 if z 1.2 and 1 else,
And FZC (z) = 1 if z 0.5 and 0 else.
Produce u from U (0,1).
If u < 0.3, set K = A ;
else if u < 0.95, set K = B ;
else set K = C.
Produce u independently from U (0, 1).
Return z = FZS1 (u).
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