Consider the reliability diagram shown below. To develop maintainability and reliability figures for the each of the three subsystems in the diagram (A, B and C) and the system, you have collected historical data (10 observations per subsystem) on the time to failure, in hours, for each of the subsystems. The data for subsystems A, B and C are shown in Tables 1 through 6, respectively.

1. Plot R(t) for the system, over the time period t=0 hours to t=1000 hours, in 50 hour increments.
2. What is the probability that the system will experience 2 or fewer failures over 100 hours?
3. Given a 26 week time period in which you operate the system for 10 hours a day, 7 days a week, what is the minimum spares complement needed in order to achieve a 95% level of confidence of having a spare on hand for subsystem A? Please take your results to the nearest percent.

A Time to Failure Time to Failure Time to Failure Observation Observation Observation 1 325 1 54 1 990 2 380 2 75 2 950 3 377 3 65 3 1100 4 395 4 71 4 1005 | 332 5 68 5 980 6 402 6 82 6 1000 7 396 7 90 7 1230 8 412 8 77 8 1130 9 423 9 92 9 980 10 420 10 72 10 1121 Table 1. Subsystem A Table 2. Subsystem B Table 3. Subsystem C Repair Time Repair Time Repair Time Observation Observation Observation 1 20 1 3 1 39 2 18 2 5 2 24 3 23 3 6 3 23 0 0 IN 4 30 4 3 4 25 5 24 5 8 5 32 6 26 6 4 6 34 7 32 7 10 7 42 8 8 8 8 24 31 29 9 9 4 9 33 10 28 10 6 10 35 Table 4. Subsystem A Corrective Maintenance Table 5. Subsystem B Corrective Maintenance Table 6. Subsystem C Corrective Maintenance A Time to Failure Time to Failure Time to Failure Observation Observation Observation 1 325 1 54 1 990 2 380 2 75 2 950 3 377 3 65 3 1100 4 395 4 71 4 1005 | 332 5 68 5 980 6 402 6 82 6 1000 7 396 7 90 7 1230 8 412 8 77 8 1130 9 423 9 92 9 980 10 420 10 72 10 1121 Table 1. Subsystem A Table 2. Subsystem B Table 3. Subsystem C Repair Time Repair Time Repair Time Observation Observation Observation 1 20 1 3 1 39 2 18 2 5 2 24 3 23 3 6 3 23 0 0 IN 4 30 4 3 4 25 5 24 5 8 5 32 6 26 6 4 6 34 7 32 7 10 7 42 8 8 8 8 24 31 29 9 9 4 9 33 10 28 10 6 10 35 Table 4. Subsystem A Corrective Maintenance Table 5. Subsystem B Corrective Maintenance Table 6. Subsystem C Corrective Maintenance