Consider the system shown below. The reliability of each process is listed at th

Question

Consider the system shown below. The reliability of each process is listed at the top of the box. Components A and B are attached separately. Component C comes in a container (E) and has a backup (D). Component F is a backup if E fails. A, B, and E (or F) have to work in order for the system to work. Please round all percentages to 4 decimal places (e.g., 45.87%). What is the reliability of the system? If $900 must be spent to fix a failed system, what is the expected failure cost of the system? Please round to the nearest dollar.

Explanation / Answer

Part (A)

  first we have to calculate the reliability of E that is...

given that C has 60% reliability so in remaing 40% case D will work with 50% reliability so,

E = 0.60 + ( 0.40 * 0.50) = 0.60 + 0.20 =0.80 or 80%

Now F has to work in remaing 20% case with 40% reliabilty hence effective reliability is = 0.20*0.40 = 0.08 or 8%

Now with A and B, E will in action either F so reliabilty of system = 0.90*0.84*0.80 + 0.90*0.84*0.08

= 0.66523 or 66.523%

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