1. Consider the following downtimes (in minutes) in the painting department of a manufacturing plant.
37.2 10.9 69.8 2.7 73.7 14.6 14.8 29.1 10.1 45.4 99.5 16.0 30.2 41.3 61.0 2.6 26.1 20.1 71.2 7.7
3.9 1.6 17.3 30.8 24.3 61.0 24.7 15.4 26.1
6.9 7.4 71.2 54.7 9.7 99.5 4.5 20.8 30.2 21.2 31.3 2.6 70.4 7.5 20.1 6.9 32.6 7.4 39.0 43.3 9.7
a. Use the chi-square test to see if the exponential distribution is a good fit to this sample data at the significance level a 1⁄4 0:05.
b. Using Arena’s Input Analyzer, find the best fit to the data. For what range of significance levels a can the fit be accepted? (Hint: revisit the concept of p-value in Section 3.11.)
2. Consider the following data for the monthly number of stoppages (due to failures or any other reason) in the assembly line of an automotive assembly plant.
12 14 26 13 19 15 18 17 14 10 11 11 14 18 13
9 20 19 9 12 17 20 25 18 12 16 20 20 14 11
Apply the chi-square test to the sample data of stoppages to test the hypothesis that the underlying distribution is Poisson at significance level a 1⁄4 0:05.
3. Let {xi} be a data set of observations (sample).
Input Analysis 139
4. The Revised New Brunswick Savings bank has three tellers serving customers in their Highland Park branch. Customers queue up FIFO in a single combined queue for all three tellers. The following data represent observed iid interarrival times (in minutes).
2.3 4.7 1.8 4.9 2.7 1.0 0.1 0.7 5.5 6.6 3.0 2.0 1.8 4.1 0.1 1.7 4.7 4.7 2.5 0.7
0.2 2.1 1.6 1.0 1.6 1.0 1.9 0.5 0.5 3.0 3.6 0.6 1.1 0.3 1.4 2.8 1.4 2.1 0.2 4.7 0.5 1.3 0.5 2.2 0.5 2.6 2.9 0.3 0.1 1.2
The service times are iid exponentially distributed with a mean of 5 minutes.
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