Question

1. A system has an overall reliability of 0.90.

a. Calculate the overall Unreliability of the system.

b. Calculate the reliability of a new system with two subsystems in series each with a reliability of 0.90.

c. Calculate the reliability of a new system with two subsystems in parallel (back-up) each with a reliability of 0.90.

d. Calculate the overall reliability of a system with two subsystems in series with the first subsystem reliability of 0.8 and second system reliability of 0.7.

e. Calculate the overall reliability of a system with two subsystems in series with the first subsystem reliability of 0.7 and second system reliability of 0.80.

f. Discuss the conditions of placing the 0.7 system first (or second).

g. Calculate the required number of inputs to produce 100 quality outputs for the systems described in part b, part c.

Answer 1

a. System unreliability or probability of failure = 1- (probability of success or reliability)

i.e, System unreliability = 1-0.9 =0.1

b. Systems connected in series with reliability 0.9 each

Given R1=0.9 and R2=0.9

Overall reliability of systems connected in series , R= R1*R2 =0.9*0.9 = 0.81

c. Systems connected in parallel with reliability of 0.9 each

Unreliability of system or probability of failure, F = 1- Reliability

Therefore, Probability of failure for both machines, F1 and F2 =1-0.9 =0.1

Resultant probability of failure , F = F1*F2 = 0.1*0.1 =0.01

Overall reliability of systems connected in paralle , R = 1-F = 1-0.01= 0.99

d. Given R1=0.8 and R2=0.7

Overall reliability of systems connected in series , R= R1*R2 = 0.8*0.7=0.56

e. Given R1=0.7 and R2=0.8

Overall reliability of systems connected in series , R= R1*R2 = 0.7*0.8=0.56

f. In series systems, failure of one system can cause impact on all the systems connected in the loop. therefore the output of the combined system is same irrespective or the sequence of series connection. We also observe that systems connected in parallel have more overall reliability than the systems connected in series due to their combined impact on overall reliability as defined in b & c.

g. For  systems defined in b), Reliability,R =0.81

Min no of inputs required to produce 100 quality inputs = 100/R =100/0.81 = 124 i.,e one has to give 124 inputs to produce 100 quality outputs

For  systems defined in c), Reliability,R =0.99

Min no of inputs required to produce 100 quality inputs = 100/R =100/0.99 = 102 i.,e one has to give 102 inputs to produce 100 quality outputs