Your wastewater treatment plant processes sludge to be sent to a landfill. These
ID: 3304906 • Letter: Y
Question
Your wastewater treatment plant processes sludge to be sent to a landfill. These are the major processes: A: secondary clarifier with a reliability of 0.98 B: gravity thickener with a reliability of 0.95 C: filter press with a reliability of 0.94 D: belt conveyor with a reliability of 0.97 Process A and B must both function for the plant to process sludge. However, Process C and D are backup systems to each other. Either one of these processes must work for the entire plant to function What is the probability that the entire plant will function as intended?Explanation / Answer
For the entire plant to function, Process A and B must work while either C or D needs to work. Therefore the combinations for the entire plant to function are ABCD', ABC'D, ABCD
P(Entire plant functions) = P(A)*P(B)*P(C)*P(D') + P(A)*P(B)*P(C')*P(D) + P(A)*P(B)*P(C)*P(D)
= 0.98*0.95*0.94*0.03 + 0.98*0.95*0.06*0.97 + 0.98*0.95*0.94*0.97 = 0.9293
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