You could go way expensive and do a time domain reflection test.  Send a
sharp square wave down each wire and wait for the reflection.  The
properties of the wires and elements being known you can calculate the
distance the wave travels in the time it takes to bounce back and
determine whether it's connected or not.

But a really cool "let's not even touch the box' way would be to
determine (experimentally) the resonant frequency of the element
attached to the cord verses seperate elements and cord.  Due to possible
cord winding differences there's a margin of error that may be quite
large, but I suspect that the difference between the two frequencies is
large enough that you could still send a wireless signal to (or through)
the toaster (package and everything) with a sweep through a small range
and determine whether the wire is connected.

This would be more expensive to develop than the first solution, but
would cost less overall.  I expect you could automate it and scan a box
a second if needed.

-Adam

Russell McMahon wrote:

>Here's a hypothetical (let's say) challenge.
>Consider it an example of a real world problem.
>Please ignore if of no interest.
>
>Problem: Propose a better test method.
>
>A manufacturer of domestic toasters finds that a large (many thousands)
>consignment of toasters has a fault.
>Many toasters are stored in a central depot but a significant number are now
>stored at several scattered locations a significant distance from the main
>storehouse. Skilled staff are probably not available at many locations.
>Conscientious and intelligent staff are deemed to be present at all
>locations (maybe a bad assumption :-) )..
>
>Each toaster has a double pole switch which disconnects the element from
>both leads of the mains cord when the toaster is plugged in and not in use.
>When the main "toasting handle" is depressed the two pole switch closes,
>passing mains power to each side of the element. (In all countries that I
>know of, all domestic toasters must have such a switch to meet regulatory
>safety requirements). In the faulty batch, in about 5% to 10% of the
>toasters, one or other pole of the two pole switch is mechanically jammed on
>due to a fault in the design and manufacturing process. The toasters that do
>not have this fault are entirely safe and meet all regulatory requirements.
>The toasters that do have this fault must be either repaired or scrapped.
>Each toaster is packed in a plastic bag and then in a cardboard carton. The
>bag is unsealed but to get access to the opening the toaster would have to
>be removed from the box. Removal and repacking takes time. The toaster has a
>non detachable cord which has a 3 pin plug (Phase, Neutral, Ground pins).
>The cord is packed at one end  of the box outside the plastic bag and the
>plug is pushed down with the cord. The plug can be pulled out a short
>distance to access its pins, if desired, without unpacking the whole cord.
>The plug is enclosed in a small plastic bag which is fastened at the cord
>end with a small rubber band.
>
>The test must reliably determine, at lowest cost in time and effort,  which
>toasters have one switch pole permanently closed so that one or other of the
>live leads is connected to the element.
>
>The brute force test solution is to unpack each toaster and test resistance
>from a point on the element to each of the two live mains pins.
>
>An alternative is to use sharp probes to poke small holes through the
>toasters' main plastic bags and plug bags to achieve the same test. This
>could be achieved without full unpacking at lower time cost but with
>slightly more skill in manipulating the conductivity tester. The
>acceptability small cosmetic damage to each bag by the test leads needs to
>be considered.
>
>SO
>
>YOU are asked for a better (faster, cheaper etc) way of doing this test.
>What do you propose?
>
>
>
>                Russell McMahon.
>
>PS - I have absolutely no official or pecuniary involvement with domestic
>toasters :-)
>
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