The PDF for the time to failure in years of the Authority bus is given by 5 algmx duadsefl At) = 0.2 – 0.02t 0t<10 yr %3D (a) Show that the hazard rate function is increasing, indicating continuous wea over time. (b) Find the MTTF. (c) Find the median time to failure. (d) Find the mode of the failure distribution. 232D
The PDF for the time to failure in years of the Authority bus is given by 5 algmx duadsefl At) = 0.2 – 0.02t 0t<10 yr %3D (a) Show that the hazard rate function is increasing, indicating continuous wea over time. (b) Find the MTTF. (c) Find the median time to failure. (d) Find the mode of the failure distribution. 232D
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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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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Please help with question 2.6 ,thanks
Transcribed Image Text:(a) What is the of within a period?
The for a is
and determine the probar
nonth of its operation.
(b) What is the design life if a reliability of 0.95 is a
The time-to-failure density function (PDF) for a system 1
f(t) = 0.01
2.3
0StS 100 days
%3D
pu
(a) R(t)
(b) The hazard rate function
(c) The MTTF
(d) The standard deviation
(e) The median time to failure
DEE
SES IMILELECvra
2.4
The failure distribution is defined by
3t2
0Sts 1000 hr
%3D
60-
(b) Compute the MTTF.
(c) Find the design life for a reliability of 0.99.
2.5 For R(t)
10
Vo.001t
= e
(a) Compute the reliability for a 50-hr mission.
(b) Show that the hazard rate is decreasing..
0マ?
HEEL 20
Given a 10-hr burn-in period, compute the reliability for a 50-hr mission.
(a) What is the design life for a reliability of 0.95 given a 10-hr burn-in?
CPS
* The PDF for the time to failure in years of the drive train on a Regional Transit
Authority bus is given by
2.6
At) = 0.2 – 0.02t 0t<10 yr
(a) Show that the hazard rate function is increasing, indicating continuous wear out
over time.
(b) Find the MTTF.
(c) Find the median time to failure.
(d) Find the mode of the failure distribution.
(e) Compute the standard deviation.
EXEUCIZE2
2.7 A Company manufactures gizmos for use on widgets. The time to failure, in years, of
these gizmos has the following PDF:
= (?)f
(t + 10)³
for t 2 0 ds bni
%3D
(P) De
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