Markov Model for TMR System with Repair

SUJITH NAIR

MARKOV MODEL

1-3λΔt3λΔt

υΔt 2υΔt

3υΔt

λΔt

1-(2λ+υ)Δt1-(2υ+λ)Δt

1-3υΔt2λΔt

DIFFERENTIAL EQUATIONS

• dP3/dt = -3λP3 + υP2

• dP2/dt = 3λP3 –(2λ+υ)P2 +2υP1

• dP1/dt = 2λP2 –(2υ+λ)P1 +3υP0

• dP0/dt = λP1 -3υP0

LAPLACE TRANSFORMS

• y3(-s-3λ) + υy2 + 1 = 0

• 3λy3 + (-s-2λ-υ)y2 +2υy1 = 0

• 2λy2 + (-s - 2υ- λ)y1 + 3υy0 = 0

• λy1 + (-s - 3υ)y0 = 0