The figure below (Figure ) shows the pipe layout in a lawn sprinkler system. Sprayers are located at every intersection of the pipe and also at the corners of the system. Thus there are 16 players. Two things can happen to a sprayer: it can break off or it can get clogged.If any one of the sprayers breaks off, a great stream of water will pour forth and the system will have failed. If one of the sprayers clogs, it will fail to water the lawn in the immediate vicinity; however, adjacent sprayers can reach the affected areas. The system is judged to be failed if any two adjacent sprayers are both failed. For one sprayer, let the probability of breakage be 0.01 and the probability of clogging be 0.05. Find the reliability of the system (the probability that it does not fail in either mode.

 

Transcribed Image Text:

6 Pipe layout in a lawn 6 Pipe layout in a lawn

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In order to calculate the reliability of the sprinkler system we need to establish the chance that i... View the full answer