The time to deliver packaged containers by a logistics company is found from samples of size 4. The mean and standard deviation of delivery times is estimated to be 140 hours and 6 hours, respectively. (a) Find the 2 sigma and 3 sigma control limits for the average delivery time. (b) Explain a type I and type II error specifically in this context. (c) If the mean delivery time shifts to 145 hours, what is the probability of not detecting this by the second sample after the shift? (d) What is the ARL? Explain

The time to deliver packaged containers by a logistics company is found from samples of size 4. The mean and standard deviation of delivery times is estimated to be 140 hours and 6 hours, respectively. (a) Find the 2 sigma and 3 sigma control limits for the average delivery time. (b) Explain a type I and type II error specifically in this context. (c) If the mean delivery time shifts to 145 hours, what is the probability of not detecting this by the second sample after the shift? (d) What is the ARL? Explain

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter10: Introduction To Simulation Modeling

Section: Chapter Questions

Problem 41P: At the beginning of each week, a machine is in one of four conditions: 1 = excellent; 2 = good; 3 =...

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At the beginning of each week, a machine is in one of four conditions: 1 = excellent; 2 = good; 3 = average; 4 = bad. The weekly revenue earned by a machine in state 1, 2, 3, or 4 is 100, 90, 50, or 10, respectively. After observing the condition of the machine at the beginning of the week, the company has the option, for a cost of 200, of instantaneously replacing the machine with an excellent machine. The quality of the machine deteriorates over time, as shown in the file P10 41.xlsx. Four maintenance policies are under consideration: Policy 1: Never replace a machine. Policy 2: Immediately replace a bad machine. Policy 3: Immediately replace a bad or average machine. Policy 4: Immediately replace a bad, average, or good machine. Simulate each of these policies for 50 weeks (using at least 250 iterations each) to determine the policy that maximizes expected weekly profit. Assume that the machine at the beginning of week 1 is excellent.
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