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IE415 Homework 4-1

1. The following data were collected for some process

a. Estimate distribution parameters if the data is assumed to be observations from a normal distribution.

b. Estimate distribution parameters if the data is assumed to be observations from a lognormal distribution.

c. Estimate distribution parameters if the data is assumed to be observations from an exponential distribution.

d. Is it reasonable to hypothesize that the data are observations from a Poisson distribution? Why?

2. Suppose you want to determine the percentages of the different part types that arrive to a machine in a day. In a period of 8 hours, you have observed 50 parts, which are of the following types shown in the table below.

a. Use the data below to estimate the percentage of part arrivals of each type.

b. What would you suggest as a theoretical distribution that may be a good representation of the part type distribution? Why?

c. Create an Arena empirical distribution to represent part type arrivals.

3. Suppose 40 observations of a random system component have been recorded as shown in the table below (these numbers are sorted).

a. Compute an estimate of the coefficient of variation. Does this estimate provide any information about possible distributions that may fit this data?

b. Using k= 8, perform a x2 goodness-of-fit (α=0.05) test that this random system component is adequately represented with a U[0,1] distribution.