I have two Markov reliability model for fault tolerant mechanism and I want to achieve the sensitivity solutions of these models through perturbation theory.
Ok, consider a system work with two parallel component (A and B) and system fails if both A & B became fail. In this model lambda (1 and 2) denotes the failure rate of each component. It is supposed that failure rate of each component obey from exponential distribution function. Reliability of the system can be achieved by solve the Markov model. I need a good theory on perturbation to achieve the sensitivity of system functioning (reliability of system) toward failure rate of component A. Bellow figure shows she Markov model of explained system.
Some paper exists about sensitivity analysis of Markov through perturbation like:
"Sensitivity and importance analysis of Markov models using perturbation analysis application in reliability studies"
In above-mentioned paper the Markov model does not have any absorbing state and I cannot use their theory.
http://hal.archives-ouvertes.fr/docs/00/70/52/34/PDF/Paper346.pdf
http://hal.archives-ouvertes.fr/docs/00/70/51/79/PDF/RESS_D_07_00095.pdf
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