6. A die forge press operates an average of 1000 hr/yr. Under a minimal repair concept, machine failures generated a nonhomogenous Poisson process having the following intensity function with t measured in operating hours: p(t) = 0.0000391t0.7. When the machine has failed, the repair time is lognormal with tmed -7.0 hours and a shape parameter of 0.8. a) Given the NHPP (Non-Homogeneous Poisson Process) time dependent parameter of this problem, p(t), does the system show reliability growth (decreasing rate of occurrence of failure) or aging (increasing rate of occurrence of failure)? b) Write the expression for and calculate the number of expected failures of the press during a mission time of 5 years, 5,000 hr, m(5,000). c) Write the expression for and calculate the MTTR, meantime to repair. Given s = 0.8, comment on the overall shape or skewness, low skew, high skew, ~ symmetric, of the Lognormal model.
6. A die forge press operates an average of 1000 hr/yr. Under a minimal repair concept, machine failures generated a nonhomogenous Poisson process having the following intensity function with t measured in operating hours: p(t) = 0.0000391t0.7. When the machine has failed, the repair time is lognormal with tmed -7.0 hours and a shape parameter of 0.8. a) Given the NHPP (Non-Homogeneous Poisson Process) time dependent parameter of this problem, p(t), does the system show reliability growth (decreasing rate of occurrence of failure) or aging (increasing rate of occurrence of failure)? b) Write the expression for and calculate the number of expected failures of the press during a mission time of 5 years, 5,000 hr, m(5,000). c) Write the expression for and calculate the MTTR, meantime to repair. Given s = 0.8, comment on the overall shape or skewness, low skew, high skew, ~ symmetric, of the Lognormal model.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
Related questions
Question
Transcribed Image Text:6. A die forge press operates an average of 1000 hr/yr. Under a minimal repair concept, machine
failures generated a nonhomogenous Poisson process having the following intensity function with t
measured in operating hours: p(t) = 0.0000391 to.7. When the machine has failed, the repair time
is lognormal with tmed -7.0 hours and a shape parameter of 0.8.
a) Given the NHPP (Non-Homogeneous Poisson Process) time dependent parameter of this
problem, p(t), does the system show reliability growth (decreasing rate of occurrence of
failure) or aging (increasing rate of occurrence of failure)?
b) Write the expression for and calculate the number of expected failures of the press during a
mission time of 5 years, 5,000 hr, m(5,000).
c) Write the expression for and calculate the MTTR, meantime to repair. Given s = 0.8,
comment on the overall shape or skewness, low skew, high skew, ~ symmetric, of the
Lognormal model.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps
Recommended textbooks for you
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON