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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) = 0.0000391t07. 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) = 0.0000391t07. 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)
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...
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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) = 0.0000391t07. 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. d) Write the expression for and calculate the MTBF, mean time between failures, for the mission time of 5 yr = 5,000 hr. e) Using this information over the 5 yr mission time, write the expression for and calculate the average inherent, steady state, Availability, Ainh of the mission time of 5 yr operating life of the press.
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) = 0.0000391t07. 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. d) Write the expression for and calculate the MTBF, mean time between failures, for the mission time of 5 yr = 5,000 hr. e) Using this information over the 5 yr mission time, write the expression for and calculate the average inherent, steady state, Availability, Ainh of the mission time of 5 yr operating life of the press.
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