For a dynamic Bayesian network (DBN) with a warm spare gate having one primary and one back-up component:

If the primary component P is active at the first time slice, then its failure rate is lambda (P) and the failure rate of back up component S1 is [alpha*lambda (S1)].

If the primary component P fails at the first time slice, then its failure rate is lambda (P) and the failure rate of back up component S1 is [lambda (S1)].

My question is, above are the conditional probabilities of primary and backup component. In a DBN, prior failure probability is also required. What will the prior failure probability of back up component? Will it be calculated using lambda (S1) or alpha*lambda (S1)?

Thank you

regards

Sanchit

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