Question

Consider the system of components connected as in the accompanying picture. Components 1 and 2 are connected in parallel, so that subsystem works iff either 1 or 2 works; since 3 and 4 are connected in series, that subsystem works if both 3 and 4 work. If components work independently of one another and P(component i works) 5 .9 for i 5 1,2 and 5 .8 for i 5 3,4, calculate P(system does not work).

Answer #1

The electrical system for an assembly line has four components
arranged in two parallel subsystems as shown in the diagram below.
Each of the four components (labeled 1, 2, 3, 4) are independent
and each has a 10% chance of failure. Because the components are
independent, the two subsystems (labeled A and B) are also
independent. If one component in a subsystem fails, then the whole
subsystem fails because the power cannot get through. However,
because there are two subsystems,...

An electrical system consist of 2 components (C1 and C2)
functioning independently, and
are set in a parallel layout. The failure time of each component
follows an exponential
distribution with rate 2 in every year.Determine the expected time
to failure for any one components and for the system.

An electrical system consists of 2 components (C1 and C2)
functioning independently and are set in a parallel layout. The
failure time of each component follows an exponential distribution
with rate 2 every year. Identify the failure density and failure
distribution of any component. Hence, calculate the probability of
any component i) failing in less than 8 months. ii) surviving after
10 months.

4. An electrical system consists of 3 components (C1, C2 and C3)
functioning independently, and are set in parallel layout. The
failure density of each component is given as below: ?(?) = { 3?
−3? , ? > 0
0 , ??ℎ??????
where X is in years.
(a) Calculate the probability that any one component will fail
in less than 3/4 years.
(b) Write the complete failure density for the model appropriate
for the system if all the components fail...

Two capacitors of 1 microfarad and 4 microfarad are connected in
a) series b) parallel. Find the equivalent capacitance in each
case.
Please include a picture, and show work pls!!! I need to
understand this!!!

An electrical system consists of 3 components (C1, C2 and C3)
functioning independently, and are set in parallel layout. The
failure density of each component is given as below:
?(?) = { 3? −3? , ? > 0 0 , ??ℎ?????? where X is in
years.
(a) Calculate the probability that any one component will fail
in less than 3 4 years.
(b) Write the complete failure density for the model appropriate
for the system if all the components fail...

A system consists of n identical components in parallel with
each component having a reliability of p. The failure events of the
components can be assumed to be independent. Compute the
reliability of the system as functions of p and n. Plot system
reliability as functions of p and n for the ranges of p = [0.9,
0.99, 0.999] and n = [3, 5, 10, 100, 1000].

Suppose that a certain system contains three components that
function independently of each other and are connected in series,
so that the system fails as soon as one of the components fails.
Suppose that the length of life of the first component, X1,
measured in hours, has an exponential distribution with parameter λ
= 0.01; the length of life of the second component, X2, has an
exponential distribution with parameter λ = 0.03; and the length of
life of the...

We have a system that has 2 independent components. Both
components must function in order for the system to function. The
first component has 9 independent elements that each work with
probability 0.92. If at least 6 of the elements are working then
the first component will function. The second component has 6
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of the elements are working then the second component will
function.
(a)
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A system consisting of four components is said to work whenever
both at least one of components 1 and 2 work and at least one of
components 3 and 4 work. Suppose that component ? alternates
between working and being failed in accordance with a nonlattice
alternating renewal process with distributions ?? and ??,?=1,2,3,4.
If these alternating renewal processes are independent, find
lim?→∞=?{system is working at time ?}.

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