Principle (Availability): The product of the individual station availabilities is a lower bound on the overall line availability

Motivation

This principle follows from the reasoning  for the availability of coupled lines.  In those lines, any failure stops the entire line and hence line availability is given by the product of the station availabilities.  In the uncoupled case, the line can continue working (for a while) after a failure occurs.  Hence, it's availability must be at least as large as that of the corresponding coupled line.  

Example

Consider the same four stations we examined in the coupled example.  That is, we have four identical stations each with individual availability of  A=0.95.  Then the availability of the coupled line is A_line = 0.95⁴ = 0.815.  If the line is uncoupled (stations can finish their current job when another station goes down), then this is a lower bound on the availability of the line.  How tight this bound is will depend on the distribution of the process times and the duration of the repair times.

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