An adhesive technologist concludes from laboratory results that a bond from a ne

Question

An adhesive technologist concludes from laboratory results that a bond from a new adhesive fails 3% of the time if oil is present on the bonding surface, 6% of the time if grit is present on the surface and 12% of the time if the surface is too smooth. The bond never fails if the surface is clean. For a particular application by an industrial customer, it is estimated that there is a 5% chance that oil will be on the surface, a 5% that grit will be present, and a 1% chance that the surface will be smooth. This customer has decided to use the new adhesive. What is the probability that the bond will be successful? If the bond is later reported to have failed, what is the probability that grit was present on the bonding surface?

Explanation / Answer

6% grit x 5% fail = .0030 failure 12% smooth  x 1% fail = .0012 failure Overall failure rate is .0057=5.7% failure, ie 94.3%success
and for a failure, the relative proportion of grit is .003/.0057 = 52% chance

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