3. The reliability function (7) of a system, where time is in units of hours, describes the time to failure random variable X, It is given that (t) = 1 (at + 1)² u(t) where is a positive constant, and (1) is the usual unit step function. a) Determine the value of the constant if is known that the MTTF is 100 hours. b) Determine the pdf fx (1) of the random variable X, c) Determine the conditional failure rate ẞ, (t) of the system and plot it as a function of time using the result of part a).
3. The reliability function (7) of a system, where time is in units of hours, describes the time to failure random variable X, It is given that (t) = 1 (at + 1)² u(t) where is a positive constant, and (1) is the usual unit step function. a) Determine the value of the constant if is known that the MTTF is 100 hours. b) Determine the pdf fx (1) of the random variable X, c) Determine the conditional failure rate ẞ, (t) of the system and plot it as a function of time using the result of part a).
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question

Transcribed Image Text:3. The reliability function (7) of a system, where time is in units of hours, describes the
time to failure random variable X, It is given that (t) =
1
(at + 1)²
u(t) where is a
positive constant, and (1) is the usual unit step function. a) Determine the value of the
constant if is known that the MTTF is 100 hours. b) Determine the pdf fx (1) of the
random variable X, c) Determine the conditional failure rate ẞ, (t) of the system and plot it
as a function of time using the result of part a).
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