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Several years ago, Baecher, de Neufville, and Paté carried out a study of reported failures of large dams around the world. They concluded that the failure rate was 0.0001 per dam-year. A dam-year is defined as one dam operating for one year. The definitions of "failure" and "large dam" are subject to dispute, but the study has become the basis for much of the reliability studies done by agencies that operate dams. Almost everyone assumes that this failure rate represents a constant failure rate (CFR) scenario even though there is good reason to believe that a bathtub curve, with higher rates of failure at the beginning and end of the life cycle, might be more appropriate. Assuming that the CFR model is accurate, answer the following: a) What is the mean time to failure (MTTF) in dam-years for the Baecher et al. model? b) If an agency manages a portfolio of 350 dams, and they are independent of each other, what is the mean time the agency can expect to carry on before a failure occurs? c) There are approximately 85,000 large dams in the United States. How many failures can we expect in a typical year?

Several years ago, Baecher, de Neufville, and Paté carried out a study of reported failures of large dams around the world. They concluded that the failure rate was 0.0001 per dam-year. A dam-year is defined as one dam operating for one year. The definitions of "failure" and "large dam" are subject to dispute, but the study has become the basis for much of the reliability studies done by agencies that operate dams. Almost everyone assumes that this failure rate represents a constant failure rate (CFR) scenario even though there is good reason to believe that a bathtub curve, with higher rates of failure at the beginning and end of the life cycle, might be more appropriate. Assuming that the CFR model is accurate, answer the following: a) What is the mean time to failure (MTTF) in dam-years for the Baecher et al. model? b) If an agency manages a portfolio of 350 dams, and they are independent of each other, what is the mean time the agency can expect to carry on before a failure occurs? c) There are approximately 85,000 large dams in the United States. How many failures can we expect in a typical year?

Practical Management Science
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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Several years ago, Baecher, de Neufville, and Paté carried out a study of reported failures of large dams around the world. They concluded that the failure rate was 0.0001 per dam-year. A dam-year is defined as one dam operating for one year. The definitions of "failure" and "large dam" are subject to dispute, but the study has become the basis for much of the reliability studies done by agencies that operate dams. Almost everyone assumes that this failure rate represents a constant failure rate (CFR) scenario even though there is good reason to believe that a bathtub curve, with higher rates of failure at the beginning and end of the life cycle, might be more appropriate. Assuming that the CFR model is accurate, answer the following: a) What is the mean time to failure (MTTF) in dam-years for the Baecher et al. model? b) If an agency manages a portfolio of 350 dams, and they are independent of each other, what is the mean time the agency can expect to carry on before a failure occurs? c) There are approximately 85,000 large dams in the United States. How many failures can we expect in a typical year?
Transcribed Image Text:Several years ago, Baecher, de Neufville, and Paté carried out a study of reported failures of large dams around the world. They concluded that the failure rate was 0.0001 per dam-year. A dam-year is defined as one dam operating for one year. The definitions of "failure" and "large dam" are subject to dispute, but the study has become the basis for much of the reliability studies done by agencies that operate dams. Almost everyone assumes that this failure rate represents a constant failure rate (CFR) scenario even though there is good reason to believe that a bathtub curve, with higher rates of failure at the beginning and end of the life cycle, might be more appropriate. Assuming that the CFR model is accurate, answer the following: a) What is the mean time to failure (MTTF) in dam-years for the Baecher et al. model? b) If an agency manages a portfolio of 350 dams, and they are independent of each other, what is the mean time the agency can expect to carry on before a failure occurs? c) There are approximately 85,000 large dams in the United States. How many failures can we expect in a typical year?
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