Suppose the lifetime in years T of a component of a solar heating system is uniformly distributed and may be anything between 0 and 25 years, i.e. T~ U(0,25). (a) Find the survivor function (t) for the component and the mean value of T. (b) Find the hazard function h(t) for these types of component and draw a sketch of h(t). Use your sketch of the hazard function to decide whether such components are NBU, NWU or neither. Assume that at some point in the future the solar heating system is replaced and this component is retained and installed into the new system. (c) Find the probability that this component (i) will need replacement within five years from the time it was installed into the new system, and (ii) will last longer than ten years from the time it was installed into the new system.
Suppose the lifetime in years T of a component of a solar heating system is uniformly distributed and may be anything between 0 and 25 years, i.e. T~ U(0,25). (a) Find the survivor function (t) for the component and the mean value of T. (b) Find the hazard function h(t) for these types of component and draw a sketch of h(t). Use your sketch of the hazard function to decide whether such components are NBU, NWU or neither. Assume that at some point in the future the solar heating system is replaced and this component is retained and installed into the new system. (c) Find the probability that this component (i) will need replacement within five years from the time it was installed into the new system, and (ii) will last longer than ten years from the time it was installed into the new system.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 33EQ
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Transcribed Image Text:Suppose the lifetime in years T of a component of a solar heating
system is uniformly distributed and may be anything between 0
and 25 years, i.e. T~ U(0,25).
(a) Find the survivor function Q(t) for the component and the mean
value of T.
(b)
Find the hazard function h(t) for these types of component and
draw a sketch of h(t). Use your sketch of the hazard function to
decide whether such components are NBU, NWU or neither.
Assume that at some point in the future the solar heating system is
replaced and this component is retained and installed into the new
system.
(c) Find the probability that this component (i) will need replacement
within five years from the time it was installed into the new
system, and (ii) will last longer than ten years from the time it
was installed into the new system.
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