Whats the best way to describe this system?

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The time to failure approach would seem to favor the 'maximum single component failure rating P(F)" as the best way to approach the issue of failure of a path of components in series. However reliability is calculated as the product of 1-P(F) over on the path. Reliability (R) vs time to first failure (TTF) are two models which give different results, so I'm not sure which model is best for this problem. However R seems more common in the literature. Assuming all components are the same age, TTF would seem to be a better measure but may be controversial.

http://media.wiley.com/product_data/excerpt/85/04700948/0470094885.pdf Go to page 5 (sec 1.2.1)

In a related issue of conditional probabilities as to what is the probability that Ai works if the system works requires one to know both P(sAi|sSys) and P(sSys|sAi). Since the probability that the component works P(sAi) and that the system works P(sSys) are not independent, the dependency of these two must be defined by isolating all paths which link a to b and have component Ai .
 
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