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California Instruments produces 3,000 computer chips per day 300 are tested for a period of 500 operating hours each. During the test, six failed: two after 50 hours, two at 100 hours, one at 300 hours, and one at 400 hours.

(1) Find FR (%) and FR(N).

(2) If 300 of these chips are used in building a large computer, how many failures of the computer can be expected per month? (Assume that a single chip failure causes the entire system to fail)

Answer :

(1) FR (%): 2%; FR(N): 6 failures.

(2) The number of expected computer failures per month is 60.

(1) To calculate the failure rate in percentage (FR %), we need to divide the number of failures by the total number of units tested and multiply by 100. In this case, out of the 300 chips tested, six failed. So, FR % = (6/300) * 100 = 2%.

To calculate the failure rate in numbers (FR(N)), we simply count the number of failures. In this case, there were six failures.

(2) Since each computer is built with 300 chips, we can use the failure rate to estimate the number of failures in a month. Given that the company produces 3,000 chips per day, we can assume that there are approximately 30 days in a month.

Therefore, the number of expected computer failures per month can be calculated by multiplying the failure rate (FR(N)) by the number of chips used in a computer and the number of months. In this case, the calculation would be: 6 failures * (3,000 chips / 300 chips) * 30 months = 60 failures.

Hence, we can expect approximately 60 failures of the computer per month.

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