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Consider the six-component system displayed below. Let r1(t), . . ., r6(t) denote the reliability functions of the components. Assume the six components operate independently.

a) Calculate the overall system reliability
b) Determine the probability of failure for component 4
c) Assess the impact of component 2's failure on the system
d) Analyze the cuμlative reliability over a specific time period

User Hogsolo
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1 Answer

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Final answer:

To calculate the overall system reliability, multiply the reliability functions of the components. The probability of failure for component 4 is obtained by subtracting its reliability function from 1. Assessing the impact of component 2's failure involves calculating the system reliability without component 2. Analyzing the cumulative reliability over a specific time period requires using the system reliability formula at that time point.

Step-by-step explanation:

a) To calculate the overall system reliability, we can use the formula: R = r1(t) * r2(t) * r3(t) * r4(t) * r5(t) * r6(t), where r1(t), r2(t), etc. denote the reliability functions of the components. Since the components operate independently, we can multiply their reliability functions.

b) To determine the probability of failure for component 4, we can subtract its reliability function from 1: P(failure component 4) = 1 - r4(t).

c) To assess the impact of component 2's failure on the system, we need to calculate the system reliability without component 2. We can use the formula from part a), but exclude r2(t) from the calculation: R_without_component_2 = r1(t) * r3(t) * r4(t) * r5(t) * r6(t).

d) To analyze the cumulative reliability over a specific time period, we can calculate the system reliability at that time point using the formula from part a).

User Mswietlicki
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