🚀 go-pugleaf

I believe there must be someone out there that has extended
the qualitative anaylsis of the situation to a more
quantitative analysis.  It is relatively easy to look past
the system you are designing to the system that it will be
incorporated into to get an idea what the cost of assembly
defects is.


BENEFITS OF TESTING 
-------------------
Most testing significantly reduces the risk of failure.  Take
for example the following scenario: We are manufacturing a
product, say a workstation, from N:=100 ICs which all have
identical and independent probability of being defect-free,
y:=99.9%.  (1000ppms is a bit low for most ICs, but still
pretty good).

With no assembly errors, the yield of the assembly will be
about Y:=y^N=90%, which for large N can be very small indeed.
By not testing the devices before assembly, we are taking the
risk that the effort expended in the assembly operation will
be wasted.  If the cost of the assembly operation and parts
is C:=$200 ($100 labor plus parts at $1 each), then risk
involved in not testing the components is R:=C(1-Y) or $20.
Let us assume that diagnosis and rework are cost well over
$20, so we just add %10(:=(1-Y)/Y) to our price and go to bed
dreaming of the millions of dollars we could save if we, or
rather our suppliers, had better yield.


WHO SHOULD BEAR THE BURDEN OF TESTING?
--------------------------------------
This brings up a crucial point.  In the bad old-days, or so I
am told, the industry had to rely on incoming inspection to
keep yields high.  This created a lot of problems for
manufacturers, because each had to invest in seperate test
equiptment for each component in thier assembly.  It far more
logical (i.e. economical) for the supplier to guarantee his
part before shipping it out, because he has the expertise to
perform the tests and can spread the cost over millions sold
rather than a few thousand bought.  Plus, if you don't test,
your customers will eventually migrate to more reliable
suppliers, unless they share a similar disinterest in guaranteeing
their product.


PRICE OF TESTING
----------------
Though I believe little is known about the cost of test
coverage I think it is fair to say that 10% of the faults in
the fault model- universe in question probably account for
90% of the failures.  This is the only reason why I can think
that functional test can compete with ATPG.  Since finding a
test-set with %100 fault-coverage for even the simplest types
of fault models is NP-complete, it is usually imposible to
guarantee 100% yield.  What I want to know is: what is the
marginal cost/benefit of testing?  I.e. how much
computational work does it take to "add" a vector to a
non-redundant test set, and how many more real defects is
that vector likely to detect?

What seems to be lacking at this point is a rigorous model of
where exactly the cost of test begins to exceede the benefits
of test.  The question posed should not be "To Test or Not
to Test?"  but "How Much Testing is Needed?"

Joel Darnauer
joel@ce.ucsc.edu