Markov chains

Question 1

Markov Analysis

Answer 1

• Stochastic process to model different system states
• Helps to visualize also complex failure modes as well as system repair. Besides, a MA is more convenient for state dependent failure rates
• The probability for a transition from one to another state is proportional to the failure rate (repair rate) λ(μ)

Question 2

Markov Analysis Steps

Answer 2

Steps:

• Identify relevant system states
• Introduce differential equations for all states
• Solve the system of differential equations

Question 3

Markov: Important Differential Equations

Answer 3

𝑃´𝑓=𝜆∙𝑃𝑐
𝑃´𝑓 Gradient of the Probability to be faulty
𝜆 Failure Rate
𝑃𝑐 Probability to be correct
𝑃´𝑐=−𝜆∙𝑃𝑐
𝑃´𝑐 Gradient of the Probability to be correct