Question

In: Operations Management

The GPS System of an autonomous 18-wheeler is controlled by a computer that has 4 major modules.

 The GPS System of an autonomous 18-wheeler is controlled by a computer that has 4 major modules. For the GPS System to function properly, all 4 modules must function together. Two of the modules have reliabilities of 0.97, and the other 2 have reliabilities of 0.98.

 A. What is the overall reliability of the 18-wheeler's GPS System?

 B. Designers have decided that the GPS System is going to be provided with

 a backup computer identical to the one currently used in the 18-wheeler to improve the system's overall reliability. Assuming the backup computer automatically functions if the primary one fails, determine the resulting reliability of the expanded system.

 C. The designers have determined that the backup computer must be activated by a switch if the primary computer fails. If the switch they want to use has a reliability of 0.95, what is the overall reliability of the system now? (Note: Both the switch and the backup computer must function in order for the backup computer to take over navigation



Solutions

Expert Solution

a.Overall reliability of the system = 0.97 x 0.97 x 0.98 x.98 = 0.9036

b. The backup computer has a reliability of = 0.9036 and it is connected in parallel

Let the resulting reliability = R

I/R = 1/0.9036 + 1/0.9036 = 2/0.9036

Or, R = 0.9036/2 = 0.4518

Resulting reliability of the expanded system = 0.4518

c.The switch is connected to the backup computer in series.

Reliability of the switch + back up computer

= Reliability of switch x Reliability of the backup computer

= 0.95 x 0.9036

= 0.8584

Let overall reliability of the system = R1

1/R1 = 1/Reliability of main system + 1/Reliability of the backup system

1/R1 = 1/0.9036 + 1/0.8584

Or, 1/R1 =1.1066 + 1.1649 = 2.2715

Or, R1 = 0.4402

Overall reliability of the system = 0.4402

keosha answered 1 year ago
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