# solution10 - 9:01 AM HW10 solution page 1 Probability for...

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10/31/03 9:01 AM HW10 solution page 1 Probability for Engineering Applications Solution to Assignment #10 1. (3 pts) The lifetime T (years) of a light bulb has pdf f T (t) = 0.25 u(t-3) [1 - u(t-7)] a.. Find the reliability function and the MTTF of the bulb. R(t) = P(T>t) = 1 - 0 (' ) ' t T ftd t = 1 t < 3 R ( t ) = 1 – (t-3)/4 = (7-t)/4 3 < t < 7 1 = 0 7 < t t 0 3 7 MTT = = 0 5 ) ( dt t R (including t = 0.0-3.0) b. Find the failure rate function r(t) = – R'(t)/R(t) = 1/(7-t) 3 < t < 7 = 0 elsewhere c. Over how many years of operation is the reliability 90%? R(t) = (7-t)/4 = 0.90 ! t = 3.40 2. A power module consists of three batteries, each of which switches on only when the previous one dies. The mean life of each battery is 1/6. The failure rate at the beginning is 3 7 1/4 t r(t)

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10/31/03 9:01 AM HW10 solution page 2 low, because the backups can kick in, but asymptotically it is only as good as a single subsystem. The lifetime of such a system is an m-Erlang random variable
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## This note was uploaded on 09/03/2008 for the course ECSE 4510 taught by Professor Woods during the Spring '03 term at Rensselaer Polytechnic Institute.

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solution10 - 9:01 AM HW10 solution page 1 Probability for...

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