Question

In a machine there are two motors, but only one motor is needed for the functioning of the machine. The reliabilities of the motors are 0.90 and 0.70. The overall reliability of the machine is \(\underline{\hspace{2cm}}\). [round off to two decimal places]

Hint:

If at least one component must work, treat the system as parallel; reliability increases significantly.

Answer 1

Correct Answer: 0.96 - 0.98

Only one motor is required → parallel reliability system. Let motor reliabilities be: \[ R_1 = 0.90, R_2 = 0.70 \] System reliability for components in parallel: \[ R_{sys} = 1 - (1 - R_1)(1 - R_2) \] Substitute: \[ R_{sys} = 1 - (0.10)(0.30) \] \[ R_{sys} = 1 - 0.03 = 0.97 \] Thus, the overall reliability lies in the range: \[ \boxed{0.96\text{ to }0.98} \]