18 State Dependent Systems 2 (2)

18 State Dependent Systems 2 (2) - MFG5350 1 Lecture...

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Unformatted text preview: MFG5350 1 Lecture Overview • State-dependent systems • Results of mid-term feedback MFG5350 2 MFG5350 3 MFG5350 4 MFG5350 5 MFG5350 6 MFG5350 7 Markov Analysis Loading Sharing Systems Standby Systems Degraded Systems STATE DEPENDENT SYSTEMS MFG5350 8 • Two-component parallel system • Dependency: if one component fails, the failure rate of the other component increases as a result of the additional load placed on it (0,0) (1,0) (0,1) (1,1) 0: Operating 1: Failed MFG5350 9 1-( + )t P (t) = e 1 2   2 1 1 2 2 +- t-( + )t P (t) = +- e- e 2 + 1 2        3 2 1 2 1 +- t-( + )t P (t) = +- e- e 1 + 1 2        R(t) = P (t)+ P (t)+ P (t) 1 2 3 Solution: Load-Sharing Systems MFG5350 10 If we let  1 =  2 =  and  1 + =  2 + =  + , then R(t) = e + 2 2- e- e-2 t +- t-2 t +       Load-Sharing Systems MFG5350 11 Component 1: Primary Component 2: Standby • Two-component parallel system • Dependency: the standby unit will have no failure or a reduced failure rate while in its standby mode. (0,0) (1,0) (0,1) (1,1) MFG5350 12 1-( + )t P (t) = e 1   2  2 1 1 2- t-( + )t P (t) = +- e- e 2 1        2 2   3- t-( + )t P (t) = e- e 1 1    2  R t = e + +- e- e- t 1 1 2- 2- t-( + )t 1 2 1 2- ( )         Standby Systems- Solution MFG5350 13 If we let  1 =  2 =  and  2- = - , then R(t) = e + e- e- t- t- t          ( )                          1 1 1 1 1 MTTF Standby Systems - identical units MFG5350...
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18 State Dependent Systems 2 (2) - MFG5350 1 Lecture...

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