PROBABILITY AND STATISTICS

PROBLEM 4.

An aerospace consulting company is working on the design of a spacecraft system composed of three main subsystems, A, B, and C. The reliability, or probability of success, of each subsystem after three periods of operation is displayed in the following table:

These reliabilities have been rounded to four significant digits. The 1.0000 in the first column means that the likelihood of the failure of subsystem B during the first day of operation is so remote that more than four significant digits are needed to indicate it.

a. Consider the case of the series system shown in Fig. 5.1. If any one (or more) of the subsystems A, B, or C fails, the entire system will fail. If Ps is the total probability of success of the system, find Ps for each of the three time periods.

Solution: For the first 24 hours,

Ps = PAPBPC
= (0.9997) (1.0000) (0.9961)
= 0.9958.

For a period of 3.3 months,

Ps = PAPBPC
= (0.8985) (0.9386) (0.9960)
= 0. 8400.

For a period of 8.5 months,

Ps = PaPbPc
=(0.6910) (0.7265) (0.9959)
= 0.5000.

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