Problem 4S-5

The guidance system of a ship is controlled by a computer that has three major modules. In order for the computer to function properly, all three modules must function. Two of the modules have reliabilities of .97, and the other has a reliability of .92.

   

a.What is the reliability of the computer? (Round your answer to 4 decimal places.)

  

  Reliability .8656   

   

b. A backup computer identical to the one being used will be installed to improve overall reliability. Assuming the new computer automatically functions if the main one fails, determine the resulting reliability. (Round your intermediate calculations and final answers to 4 decimal places.)

  

  Reliability .9819   

   

c. If the backup computer must be activated by a switch in the event that the first computer fails, and the switch has a reliability of .97, what is the overall reliability of the system? (Both the switch and the backup computer must function in order for the backup to take over.) (Round your intermediate calculations and final answers to 4 decimal places.)

   

  Reliability .9784   

rev: 03_15_2012

Explanation:

a.

.97 x .97 x .92 = .8656

b.

.8656 + (1 – .8656) x .8656 = .9819

[i.e., P(work) + P(not work) x P(backup works)]

c.

.8656 + [(1 – .8656) x .97 x .8656] = .9784

[i.e., P(work) + [P(not work) x P(switch works) x P(backup works)]

Problem 4S-19

Determine the availability for each of these cases:

    

a. MTBF = 50 days, average repair time = 8 days.(Round your answer to 2 decimal places.)

   

  Availability .86   

   

b.MTBF = 270 hours, average repair time = 4 hours.(Round your answer to 2 decimal places.)

    

  Availability .99   

Explanation:

Availability=

MTBF

MTBF + MTR

a.

50

= .86

50 + 8

b.

270

= .99

270 + 4