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Maximizing mean-time to failure in k-resilient systems with repair

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2 Author(s)
Fridman, J. ; Dept. of Electr. & Comput. Eng., Northeastern Univ., Boston, MA, USA ; Rangarajan, S.

A k-resilient system with N components can tolerate up to k component failures and still function correctly. We consider k-resilient systems where the number of component failures is a constant fraction of the total number of components, that is k=N/c and c is a constant such that 2⩽c<∞. Under a Markovian assumption of constant failure and repair rates, we compute the system size Nmax at which the mean-time to failure (MTTF) for such a system is maximized. Our results indicate that Nmax can be expressed in terms of constant c and parameter ρ as Nmax=K(c,ρ)/ρ, where ρ=λ/μ and K(c, ρ) is a function of c,ρ. In addition, we have found that the variation of Nmax over the whole range of c is remarkably small, and as a result, even if the resilience k of a system as a function of N varies widely, the system size at which the MTTF is maximized is within the range 0.36/ρ and 0.5/ρ. We validate our results through event-driven simulation, and, in addition, examine the behavior of systems with Weibull distributed failure times

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Computers, IEEE Transactions on  (Volume:46 ,  Issue: 2 )