Question

A manufacturer of disk drives for notebook computers wants a MTBF of at least 50,000hours. Recent test results for 12 units were one failure at 8,000 hours, two at 20,000 hours, and two more at 48,000 hours. The remaining units were still running at 60,000 hours. Determine the following:

a)Percent of failures? =

b) Number of failures per unit-hour =

c) The mean time between failures? (MTBF) is the expected time between a repair and the next failure of a component, machine, process, or product. MTBF is the reciprocal of FR(N): MTBF at this time in testing? = (round your response to the nearest whole? number).

Answer 1

Solution-

MTBF or theta = (total time)/total failures

Lets us calculate total time by multiplying the number of units by the time before they failed-

1 failed at 8000 hours = 8000*1 = 8000

2 failed at 20000 hours each = 20000*2 = 40000

2 failed at 48000 hours each = 48000 * 2 = 96000 hours

Rest (12-(1+2+2) = 7) still running at 60000 hours = 60000*7 = 420000

Total running time = 8000 + 40000 + 96000 + 420000 = 564000

Total number of failures = 1 + 2 + 2 =5

Therefore, MTBF = Total running time/total failures = 564000/5 = 112800

a. percent of failures = (total failures/total products tested)*100 = (5/12)*100 = 41.67

b. Number of failures per unit hour = total failures/total running time = 5/564000 = 0.00000886524 failures per unit hour.