Question

The following system has three components. Component 1 has 96.7% reliability, component 2 has 78% reliability with a 70% reliable backup, and finally component 3 has 99.99% reliability. If the system costs $850 to fix every time it breaks down, what is the expected fixing cost if the system runs for 1000 times?

Answer 1

For System C:

Reliability of components with backup = 0.95 + (1 – 0.95)0.90 = 0.995

Reliability of system C = (0.995)(0.995)(0.95) = 0.94

Probability of failure of system C = 1 - 0.94 = 0.0594

Cost of failure = $10,000

Expected cost of failure = 0.0594 x 10,000 = $595

Total component cost of System C = (# of 0.95 component) x ($2000) + (# of 0.90 component) x ($1000) = 3 x $2000 + 2 x $1000

Total component cost of System C = $8,000

Approximate cost of failure of system C = Expected cost of failure + Total component cost = $595 + $8,000

Approximate cost of failure of system C = $8,595