Derive the differential equations for the state probabilities
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Derive the differential equations for the state probabilities

QUESTION 4 

Consider an electrical component that can fail in two modes: short-circuit and open-circuit modes. Develop a Markov diagram using the following parameters: 

λ0, μ0 failure and repair rates for open-circuit mode 

$$ \lambda _s, \mu_s$$ failure and repair rates for short-circuit mode

a. Derive the differential equations for the state probabilities. 

b. Find the steady-state probabilities and calculate the steady-state availability. 

c. Now consider the short-circuit failure to be non-repairable. Develop an expression for the MTTF.

d. Suppose now that both failure modes are non-repairable. What is the reliability as a function of time? 

Hint
Statisticsa.) A defferential equation reffers to the relation of one or more derative functions. The functions normally represent quantities in physical, the rates of change are represented by the derivatives. The formulae is dy/dx = f(x). State probabilities is the ratio of nonconditional probabilities...
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