An engine fails due to either Crankshaft failure, lubrication failure or journal

Question

An engine fails due to either Crankshaft failure, lubrication failure or journal bearing failure. Probability of engine failure given the crankshaft fails is 0.45. Probability of engine failure given the lubrication fails is 0.85. Probability of engine failure given the bearing fails is 0.6. The probability that an engine fails due to crankshaft is 0.3. The probability that an engine fails due to lubrication is 0..5. The probability that an engine fails due to bearing is 0.2. If a transmission fails, what is the most likely cause of failure? Explain your answer.

Explanation / Answer

F = Failure

C = Crankshaft

L = Lubrication

B = Bearing

P ( F | C ) = 0.45

P ( F | L ) = 0.85

P ( F | B ) = 0.60

P ( C ) = 0.3

P ( L ) = 0.5

P ( B ) = 0.2

P ( C | F ) = (0.3*0.45)/((0.3*0.45)+(0.5*0.85)+(0.2*0.60)) = 0.1985

P ( L | F ) = (0.5*0.85)/((0.3*0.45)+(0.5*0.85)+(0.2*0.60)) = 0.6250

P ( B | F ) = (0.2*0.6)/((0.3*0.45)+(0.5*0.85)+(0.2*0.60)) = 0.1765

P ( L | F ) > P ( C | F ) > P ( B | F )

Answer: The most likely cause of failure is lubrication failure.

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