A type of system that is employed in engineering work is a group of parallel com

Question

A type of system that is employed in engineering work is a group of parallel components or a parallel system. In this more conservative approach, the probability that the system operates is larger than the probability that any component operates. The system fails only when all components fail. Consider a situation in which there are 4 independent components in a parallel system with a probability of operation given to the right. What is the probability that the system does not fail? Component 1: 0.85 Component 2: 0.98 Component 3: 0.80 Component 4: 0.95 The probability that the system does not fail is (Simplify your answer.)

Explanation / Answer

P(system does not fail) = 1- P(system fails)

P(system fails) = P(component 1 fails)*P(component 2 fails)*P(component 3 fails)*P(component 4 fails)

P(system fails) = (1-0.85)*(1-0.98)*(1-0.8)*(1-0.95) = 0.00003

P(system does not fail) = 1- 0.00003 = 0.99997~1

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