Maintainability for a Subsystem: Your team is charged with developing a subsystem that has a 90% probability of operating for 5 years.
a) If the subsystem failure times are Lognormal with a shape parameter of s = 0.7, predict the MTTF consistent with the subsystem requirement.
b) If the subsystem fails, it must be repaired within 4 hr or the system of which the subsystem is a part would more likely fail and increase the system risk to an unacceptable level. If the repair time is Lognormal with a MTTR = 2 hr and with a shape parameter of 1, calculate the probability that the subsystem will be repaired within the required time.
Note that in this problem we could also consider SAD, which for a high resilience system should be ~ 0 that is implicitly assumed in this problem. But in your professional work, bring focus to measuring organizational factors and estimate SAD as part of the expected down time for each of your critical components as identified through your risk assessment.
c) Find the most probable repair time, i.e., the mode of the repair time distribution. We have discussed in class that the mode of a repair distribution is an important point value representative of the distribution in which the majority of repairs are distributed in the region of the mode with relatively few short repairs and even fewer very long repairs that appear in the long tail to higher t values.