Suppose eight integrated circuits are placed on lifetesting

Suppose eight integrated circuits are placed on life-testing and failures occur at 100, 200, 400, 404, 450, and 500 hours, with two randomly selected non-failing units removed at 200 and 410 hours for destructive examination and comparison with the failed units at 200 and 450 hours. Compute the product limit estimate of reliability at 450 hours. Hint: Section IV - 43/44 a. 0.125 b. 0.167 c. 0.225 d. 0.300 NEED Calculation PLZ

Solution

The use of a high resolution thermal plotter has shown operating life failures to be due to localized heating resulting from IR drops at constrictions in the aluminum metalization. Storage problems result from a significant decrease in conductivity of the metalized layer. Also, reaction of aluminum with silicon dioxide, which is thermodynamically feasible, occurs to a significant extent during high temperature storage. In any application of Al metalization, even a localized Al-SiO2 interaction is very undesirable, because it can adversely affect the electrical conductivity of the Al film, or because it can result in penetration or in decrease in thickness of the Si02 layer. These effects can change the electrical characteristics of the device on which they occur.

In this case, failure rate per hour is defined as the number of failures divided by total operating hours.

Two hundred units of a particular component were subjected to accelerated life testing equivalent to 2,500 hours of normal use. One unit failed after 1,000 hours and another after 2,000 hours. All other units were still working at the conclusion of the test. The failure rate per hour = 2/[198 (2,500) + 1,000 + 2,000] = 0.000004016 per hour Note that this formula assumes constant failure rate over time.

The inverse of failure rate per hour is mean time to failure (MTTF), the average length of time (in hours) before failure.

For repairable items, a similar term, mean time between failures (MTBF), is usually used. MTBF is the average time from the up time after the repair following a failure to the next failure.

The Exponential distribution is completely described using a single parameter, its average, in this case the mean time to failure (or between failures). Using the symbol T to represent length of service, the reliability or probability that failure will not occur before time T (i.e., the area in the right tail) is easily determined by: Reliability = P(no failure before T) = e-T/MTTF where e 2.7183 T = Length of service before failure MTTF = Mean time to failure The probability that failure will occur before time T is 1 minus reliability: P(failure before T ) = 1 eT/MTTF Selected values of eT/MTTF (i.e., reliability),