w we have two each of components A, B, and C. So long as at least one component of each pair is working, the system is working. We call this a parallel system. The use of parallel subsystems for improved base-station reliability, is shown in Fig. 4.7. We can model a two-element parallel system with three states, BOTH-WORKING, ONE- WORKING, and BOTH-FAILED, as shown in Fig. 4.8. We assume that each of the two com- ponents has the same l failure rate as before and the same repair rate as before. The reason we have 2X instead of 1 as the rate from BOTH-WORKING to ONE-WORKING is that there are two components, either one of which could fail. We also assume that the re- pair in the FAILED state will fix both components. We can set up three equilibrium equa- tions by insisting that the probability flows are equal in and out of the FAILED state and Figure 4.7 Six components in a series and parallel system. Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. The Base Station Key Radio Concepts Working Working Failed Figure 4.8 Three-state component reliability diagram. the ONE-WORKING state and that the three probabilities add up to 1, as shown in Eq. (4.2)¹0 upo = NP1 (A + u) p1 = (2x)p2 (4.2) Po + p1 + P2 = 1 where Po = probability of being in FAILED state P1 = probability of being in ONE-WORKING state P2 = probability of being in BOTH-WORKING state The solution for the probability of being in the FAILED state is 2X 21 + This redundancy drops the outage time for our example component from 3.2 to 0.2 per- cent, a major improvement in reliability for a factor of 2 in equipment cost. This example has both components of the parallel system able to fail in the BOTH- WORKING state. We call this a hot spare because both components are actually running. An alternative design has a primary unit running and a secondary unit that stays off un- til it is needed. W