The hazard function of a system is given by:
h(?) = ? ∗ ? , ?...
The hazard function of a system is given by:
h(?) = ? ∗ ? , ? > 0 , ? ≥ 0
Find the expressions of probability density function, median
time to failure, and mode
Consider the joint density function f (x, y) = 1 if 0<=
x<= 1; 0<=y<= 1....
Consider the joint density function f (x, y) = 1 if 0<=
x<= 1; 0<=y<= 1. [0 elsewhere]
a) Obtain the probability density function of the v.a Z, where Z =
X^2.
b) Obtain the probability density function of v.a W, where W =
X*Y^2.
c) Obtain the joint density function of Z and W, that is, g (Z,
W)
The reliability of a component is modelled by a two parameter
Weibull distribution with a shape...
The reliability of a component is modelled by a two parameter
Weibull distribution with a shape factor (β)
equal to 2, and scale factor (η) equal to 100 weeks. The
reliability function (R(t)) as a function of time
(weeks) is:
?(?) = ?-(t/η)^β
a) Explain what the reliability function represents, and when it
might be used? (1 mark)
b) If the component has survived for 20 weeks of operation, what is
the probability that the
component will fail in the...
Reliability
1. A system has two failure modes, One mode is caused
by external environmental events...
Reliability
1. A system has two failure modes, One mode is caused
by external environmental events where the value of the failure
value is a constant of -0.008 per year. The second failure mode is
characterized by wearouts, which have a Weibull distribution with
10-year age characteristics and shape parameters - 1.8 The system
life is designed for 5 years.
a) Determine system reliability
b). If Preventive Maintenance is used in wearout failure mode
restoration to get good new conditions,...
2. (12 pts.)If r"(t) = 〈1, t, sin(t)〉 , r'(0) = 〈2, 3, 1〉 and
r(0)...
2. (12 pts.)If r"(t) = 〈1, t, sin(t)〉 , r'(0) = 〈2, 3, 1〉 and
r(0) = 〈1, 0, 1〉, find r(t).
A population of insects currently numbers 22,800 and is
increasing at a rate of R(t) =...
A population of insects currently numbers 22,800 and is
increasing at a rate of R(t) = 1225e^0.14t insects/week. If the
survival function for the insects is S(t) = e^−0.2t, where t is
measured in weeks, how many insects are there after 12 weeks?
For the following data set, tabulate and plot the nonparametric
the a) reliability function, b) probability...
For the following data set, tabulate and plot the nonparametric
the a) reliability function, b) probability density function, and
c) hazard function. There are 25 systems on test with the following
times to failure.
5, 6, 8, 10, 11, 12, 15, 20, 24, 29, 33, 40, 43, 50, 54, 58, 60,
60, 61, 62, 62, 63, 64, 65, 66
What observations would you make based on your analysis?