15 state dependent system (2) - Lecture Overview...

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MFG 5350 1 Lecture Overview State-dependent systems Quiz #3
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MFG 5350 2 October 20, 2008 (next Monday) Mid-term exam Close book and close notes 10 pages for reference
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MFG 5350 3 Due Oct 17 (this Friday) before 5:00PM Homework 4
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MFG 5350 4 Markov Analysis Loading Sharing Systems Standby Systems Degraded Systems STATE DEPENDENT SYSTEMS
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MFG 5350 5 Assumptions: The probability that a system will undergo a transition from one state to another state depends only on the current state of the system and not on any previous states The transition probabilities do not change over time (transition rate is constant). Markov Analysis
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MFG 5350 6 Markov Analysis STATE COMPONENT 1 COMPONENT 2 1 operating (0) operating (0) 2 failed (1) operating (0) 3 operating (0) failed (1) 4 failed (1) failed (1) Two Components (0,0) (1,0) (0,1) (1,1) Define: i constant failure rate for component i.
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MFG 5350 7 Two-Component System Let Pi(t) = probability of being in state i at time t 1 2 3 4 P (t)+ P (t)+ P (t)+ P (t) = 1 s 1 R (t) = P (t) For two components in series: (t) P + (t) P + (t) P = (t) R 3 2 1 s For two components in parallel:
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