MintJulep, I'm not sure if your example is taken from real life, but I can think of real products that are successful that have each of your quality limits individually.
"If I ask you to provide me a product that fails to perform as intended 76% of the time,"
This is failure to perform during the mission. 76% might be an acceptable failure rate where the product depends on a scattergun or bulk property - eg microballoons as fillers in resins. Filtering systems might only be 24% efficient, per stage. But with enough of them you can build atomic bombs. Another class of example would be where the performance of the vital few is of far greater impact than the majority.
" requires twenty hours of maintenance for each hour of use,"
Modern fighter planes, or torpedoes, would easily exceed this
" and, when it does work, 50% of the product produced must be rejected and you provide me exactly that,"
One example might be a tyre and wheel balancing machine. I'm not sure if 50% is a reasonable estimate of the number of wheels that need a second go, but it must be of that order.
" have you provided a quality product?"
If those were sensible and compatible customer defined specifications, then I believe, yes, it is a quality product. The last one is the most interesting, since the high reject rate has an enormous effect on the manufacturer's costs, yet with 100% testing, it has no effect on the customer. At the same time this is not regarded as an acceptable solution where I work, since any failure of the inspection process will result in poor product. There's also the question of how exactly the pass mark is set - how sure are we that a 49th percentile part is a failure in the cutomer's eyes, and a 51% is satisfactory?
Cheers
Greg Locock