1 Accept or discard?
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Let’s start with a question that could arise in a particular engineering problem:
A particular kind of electronic component is produced on an assembly line. At the end of the line, there is an automated inspection device that works as follows with every newly produced component coming out of the line.
The inspection device first makes some tests on the new component. The tests give an uncertain forecast of whether that component will fail within its first year of use, or after.
Then the device decides whether the component is accepted and packaged for sale, or discarded and thrown away.
When a new electronic component is sold, the manufacturer has a net gain of \(1\$\), and that’s the net gain if the component works for at least a year. If the component fails within a year of use, however, the manufacturer incurs a net loss of \(11\$\) (12$ loss, minus the 1$ gained at first), owing to warranty refunds and damage costs to be paid to the buyer. When a new electronic component is discarded, the manufacturer has \(0\$\) net gain.
For a new electronic component just come out of the assembly line, the tests of the automated inspection device indicate that there is a \(10\%\) probability that the component will fail within its first year of use.
Should the inspection device accept the new component? or discard it?
Try to give and motivate an answer: