2. Suppose that the cumulative distribution function of the lifetime of a piece of operating equipment is given by F(t) = 1 – e-0.61 – 0.6te¬0.61 where t is measured in years of continuous operation. a. Determine the reliability function. b. Determine the failure rate function. c. What is the probability that this piece of equipment fails in the first year of operation? d. What is the probability that this piece of equipment fails in the fifth year of operation? e. What proportion of the equipment surviving four years fails in the fifth year? (Calculate without using the failure rate function.) f. Does r(4) closely approximate the answer to part (e)? Why or why not? g. What proportion of the equipment surviving four years fails in the first month of the fifth year? (Calculate using the failure rate function.)
2. Suppose that the cumulative distribution function of the lifetime of a piece of operating equipment is given by F(t) = 1 – e-0.61 – 0.6te¬0.61 where t is measured in years of continuous operation. a. Determine the reliability function. b. Determine the failure rate function. c. What is the probability that this piece of equipment fails in the first year of operation? d. What is the probability that this piece of equipment fails in the fifth year of operation? e. What proportion of the equipment surviving four years fails in the fifth year? (Calculate without using the failure rate function.) f. Does r(4) closely approximate the answer to part (e)? Why or why not? g. What proportion of the equipment surviving four years fails in the first month of the fifth year? (Calculate using the failure rate function.)
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
Related questions
Question
![2. Suppose that the cumulative distribution function of the lifetime of a piece of
operating equipment is given by
F(t) = 1 – e-0.61 – 0.6te¬0.61
where t is measured in years of continuous operation.
a. Determine the reliability function.
b. Determine the failure rate function.
c. What is the probability that this piece of equipment fails in the first year of
operation?
d. What is the probability that this piece of equipment fails in the fifth year of
operation?
e. What proportion of the equipment surviving four years fails in the fifth year?
(Calculate without using the failure rate function.)
f. Does r(4) closely approximate the answer to part (e)? Why or why not?
g. What proportion of the equipment surviving four years fails in the first month
of the fifth year? (Calculate using the failure rate function.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F53fdd0f3-2786-481a-99a1-d1be52661933%2F53b208b6-e69f-4723-b249-aa4cbf2c53ce%2Fcdptyjk9.png&w=3840&q=75)
Transcribed Image Text:2. Suppose that the cumulative distribution function of the lifetime of a piece of
operating equipment is given by
F(t) = 1 – e-0.61 – 0.6te¬0.61
where t is measured in years of continuous operation.
a. Determine the reliability function.
b. Determine the failure rate function.
c. What is the probability that this piece of equipment fails in the first year of
operation?
d. What is the probability that this piece of equipment fails in the fifth year of
operation?
e. What proportion of the equipment surviving four years fails in the fifth year?
(Calculate without using the failure rate function.)
f. Does r(4) closely approximate the answer to part (e)? Why or why not?
g. What proportion of the equipment surviving four years fails in the first month
of the fifth year? (Calculate using the failure rate function.)
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