Question

Q1. What are the sign of component failure?

Answer #1

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The failure time of a component is believed to be an Exponential
random variable. A component life test is performed, with the goal
being to make inferences about the mean time to failure. One
component is in operation at all times; in the event of failure,
the failed component is immediately replaced by a new component.
Observation begins at time T = 0 and ends at time T = 1,840
minutes, during which time 14 failures occur. Which is the...

The
failure time of a component is a random variable with an
exponential distribution that has a mean of 777,6 hours. What is
the probability that the component will still be working after 2014
hours ?

The failure time, in weeks, of a component is a random variable
with a Weibull distribution with parameters a=7.49 and b=1.28. What
is the probability that the component will still be working after
1.0 weeks?

In airline applications, failure of a component can result in
catastrophe. As a result, many airline components utilize
something called triple modular redundancy. This means that a
critical component has two backup components that may be utilized
should the initial component fail. Suppose a certain critical
airline component has a probability of failure of 0.0057 and the
system that utilizes the component is part of a triple modular
redundancy. (a) Assuming each component's failure/success is
independent of the others, what...

Suppose that a system has a component whose time in years until
failure is nicely modeled by an exponential distribution. Assume
there is a 60% chance that the component will not fail for 5
years.
a) Find the expected time until failure.
b) Find the probability that the component will fail within 10
years.
c) What is the probability that there will be 2 to 5 failures of
the components in 10 years.

Consider a system with one component that is subject to failure,
and suppose that we have 90 copies of the component. Suppose
further that the lifespan of each copy is an independent
exponential random variable with mean 30 days, and that we replace
the component with a new copy immediately when it fails.
(a) Approximate the probability that the system
is still working after 3600 days.
Probability ≈≈
(b) Now, suppose that the time to replace the
component is a...

Assume that a component passes a test is 0.85 and that
components perform independently. What is the probability that the
third failure will occur on the tenth component tested?
Consider the distribution of problem 1. Graph this
distribution.

You are a failure analysis engineer who must certify the
integrity of an engineering component. Your component manufacturer
has informed you that the plane strain fracture toughness of the
component is measured to be as high as 140 ???√? and certifies that
the surface cracks observed in the components are not bigger than
0.01 mm. During service, this component is to be continuously
cycled at 3000 revolutions per minute between compressive and
tensile stresses of 350 MPa. Assume that ?...

a.Two charges are placed on the x axis. One charge (q1 = +8.12
µC) is at x1 = +3.20 cm and the other (q2 = −20.8 µC) is at x2 =
+8.63 cm.
Calculate the x-component of the net electric field at x = 0 cm,
including the sign.
b.Calculate the x-component of the net electric field at x = 6
cm

Graph this distribution in R studio, please! Assume that a
component passes a test is 0.85 and that components perform
independently. What is the probability that the third
failure will occur on the tenth component tested?

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