Suppose the lifetime in years T of a component of a solar heating system is uniformly...
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Suppose the lifetime in years T of a component of a solar heating system is uniformly distributed and may be anything between 01 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. (d) Find the probability density function of the total lifetime of this component, and calculate both (i) its mean total lifetime, and (ii) its variance. (e) If the heating system is replaced after twenty five years, how many times should you expect the component to be replaced in that time? [3] [5] [5] [3] Suppose the lifetime in years T of a component of a solar heating system is uniformly distributed and may be anything between 01 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. (d) Find the probability density function of the total lifetime of this component, and calculate both (i) its mean total lifetime, and (ii) its variance. (e) If the heating system is replaced after twenty five years, how many times should you expect the component to be replaced in that time? [3] [5] [5] [3]
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a The survivor function Qt for the component can be calculated using the uniform distribution Since the components lifetime is uniformly distributed between 0 and 25 years the survivor function is giv... View the full answer
Related Book For
Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
Posted Date:
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