Question

Mary’s Motorcycles produces custom, made-to-order motor bikes. The last stage before shipping the finished bikes is to test the air pressure in the tires. The Machine that tests the tire pressure has a Tester for the Front wheel, and a second Tester for the Back wheel, both of which must work in order to confirm the bike is ready for shipment. The Front Tester works reliably 16 out of every 20 times it’s turned on, and the Back Tester works reliably 18 in every 20 attempts.

If an identical backup is added to the Front Tester with a switch that works 90% of the time, what is the Machine’s reliability? (.8496 Or 89.46%)

If an identical backup is added to the Back Tester with a switch that works 85% of the time, what is the Machine’s reliability? (.7812 Or 78.12%)

If a backup is added to the Front and Back Testers with identical reliabilities, respectively, each with a switch that works 92% of the time, what is the Machine’s reliability? (.9309 Or 93.09%)

I need help solving the problem. The answers are in parenthesis

Answer 1

A)If an identical backup is added to the Front Tester with a switch that works 90% of the time, what is the Machine’s reliability? (.8496 Or 89.46%)

16 out of 20 times then ,

Number of failure 20-16= 4

Operating time 90%

Reliability = Total operating hours / number of failures

= 90%/4

= 90/4*100

=90/400= 0.225

Reliability of front wheel is 0.225 or 22.5%

B)If an identical backup is added to the Back Tester with a switch that works 85% of the time, what is the Machine’s reliability? (.7812 Or 78.12%)

18 out of 20 attempt

Number of failures= 20-18= 2

Total operating hours = 85%

Formula of Reliability = Total operation hours / number of failures

= 85%/2

= 85/2*100

= 85/200

= 0.425 or 42.5%

Reliability of back wheel is 0.425 or 42.5%

C)If a backup is added to the Front and Back Testers with identical reliabilities, respectively, each with a switch that works 92% of the time, what is the Machine’s reliability? (.9309 Or 93.09%)

Identical reably of both wheels = 16 out of 20 front tester, 18 out of 20 back wheel .

Then adding both , 16+18 out of 20+20

34 out of 40

Number of failures = 40-34= 6

Total operating hours= 92%

Formula for Reliability= Total operating hours/ Number of failures

= 92%/6

= 92/6*100

= 92/600

=0.1533 or 15.33%

Reliability of both wheels is 0.1533 or 15.33%

Thank you.