MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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2. A manufacturer has a machine that, when operational at the beginning of a day, has a probability of 0.1 of
breaking down sometime during the day. When this happens, the repair is done the next day and completed at
the end of that day.
The one-step transition matrix is obtained from Week 12 assignment Problem #3:
State O-operational, state 1 – break down, state 3 -- repaired
0.9 0.1 0
0
0 1
0.9
0.1 0
P =
(a) Use the approach described in Sec. 29.6 to find the 歭 (the expected first passage time from state i to state j)
for all i and j. Use these results to identify the expected number of full days that the machine will remain
operational before the next breakdown after a repair is completed.
(b) Now suppose that the machine already has gone 20 full days without a breakdown since the last repair was
completed. How does the expected number of full days hereafter that the machine will remain operational
before the next breakdown compare with the corresponding result from part (b) when the repair had just been
completed? Explain.
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Transcribed Image Text:2. A manufacturer has a machine that, when operational at the beginning of a day, has a probability of 0.1 of breaking down sometime during the day. When this happens, the repair is done the next day and completed at the end of that day. The one-step transition matrix is obtained from Week 12 assignment Problem #3: State O-operational, state 1 – break down, state 3 -- repaired 0.9 0.1 0 0 0 1 0.9 0.1 0 P = (a) Use the approach described in Sec. 29.6 to find the µ¡¡ (the expected first passage time from state i to state j) for all i and j. Use these results to identify the expected number of full days that the machine will remain operational before the next breakdown after a repair is completed. (b) Now suppose that the machine already has gone 20 full days without a breakdown since the last repair was completed. How does the expected number of full days hereafter that the machine will remain operational before the next breakdown compare with the corresponding result from part (b) when the repair had just been completed? Explain.
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