This is a Class Lecture Slide for a Course on 'System Reliability'. A Short Description of the Markov Model for TMR System with Repair, and its Related Equations.

1. Markov Model for TMR System
with Repair
SUJITH NAIR

2. MARKOV MODEL
1-3λΔt
3λΔt
υΔt 2υΔt
3υΔt
λΔt
1-(2λ+υ)Δt
1-(2υ+λ)Δt
1-3υΔt2λΔt

3. DIFFERENTIAL EQUATIONS
• dP3/dt = -3λP3 + υP2
• dP2/dt = 3λP3 –(2λ+υ)P2 +2υP1
• dP1/dt = 2λP2 –(2υ+λ)P1 +3υP0
• dP0/dt = λP1 -3υP0

4. 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