8. A machine in use is replaced by a new machine either when it fails or when

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8. A machine in use is replaced by a new machine either when it fails or when it reaches the age of T years. If the lifetimes of successive machines are independent with a common distribution F having density f , show that

(a) the long-run rate at which machines are replaced equals

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(b) the long-run rate at which machines in use fail equals

image text in transcribed

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Introduction To Probability Models

ISBN: 9780123756862

10th Edition

Authors: Sheldon M Ross

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Question Posted: Sep 16, 2024 04:01 AM

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8. A machine in use is replaced by a new machine either when it fails or when

Question:

T xf (x) dx+ T(1- F(T))

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Introduction To Probability Models

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