a) A manufacturer of capacitors performs testing and finds that the capacitors e
ID: 2082810 • Letter: A
Question
a) A manufacturer of capacitors performs testing and finds that the capacitors exhibit a constant failure rate with a value of 4x10-8 failures per hour. What is the reliability that can be expected from the capacitors during the first 2 years of their field life?
b) A customer performs the test on the capacitors considered in part a. A sample size of 1000 capacitors is used and tested for the equivalent of 5000 hours in an accelerated test. How many capacitors should the customer expect to fail during their test?
Explanation / Answer
a) Failure rate = 4 * 10-8 per hour
Failure in 2 years = Hours in 2 years * Failure rate per hour
Hours in 2 years = 2 * 365 * 24 = 17520 hours ( as 1 year = 365 day & 1 day = 24 hour)
Failure in 2 years = 2 * 365 * 24 * 4 * 10-8 = 7.008 * 10-4
Reliability = ( 1 - Failure in 2 years)
= ( 1 - (7.008 * 10-8)) = 0.9992992
Expected Realiability ( in % ) = 0.9992992 * 100
= 99.929992
= 99.923 %
So, the expected reliability is 99.923 %.
b) Sample Size = 1000
Testing Equivalent hours = 5000
Failure rate = 4 * 10-8 per hour
Expected Failure = Failure Rate * Sample size * Testing equivalent hours
= 4 * 10-8 * 1000 * 5000
= 0.2
No. of capacitor can't be fraction. So, Expected failure is 1.
So, customer can expect 1 capacitor to fail during the test.
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