I also agree with the assessment of no 200% inspection.  I actually lean much farther to "no inspection".

As far as the analysis of profit/loss both analyses so far are a bit off.  Both are valid arithmetic, but not arranged correctly.

The first pass is pretty straightforward and getting to "net income" of $743,750 I think we all agree.

Now come the accounting games:  one game is to take the incremental income and subtract the resulting cost and get ~$30k loss. While mathematically correct, this misses that the bad ones were getting scrapped anyhow and already accounted for.  We just added inspection cost to confirm these failures (which we've chosen to leave out...more on that later).  The next game is to show the reinspection as the gross recoup of the good parts (the $1.75 above).  while this is mathematically correct, it neglects that $62,725 is still being scrapped and the additional $18k in market losses, which results in a benefit of ~$65k increase in gross profit. See the analysis below

Now to inspection costs: with the scales given, I would venture that $0.05 inspection (including handling, storage, transportation to inspection, etc.) is a fair cost per part to inspect.  Given that the cost to inspect the 1,000,000 the first time around is $50k and the subsequent 135,000 would add an additional $6,700.  Adding these costs to the model essentially gives a "neutral" cost to the overall inspection (with the exception of that liability lawsuit for knowingly and purposefully introducing additional defects into the market place).

With the inspection cost "neutral" to a bottom line, the impact of increasing effectiveness of inspection becomes almost impossible to define and justify.  Whereas the reduction of defects directly hits the bottom line (and doesn’t incur the inspection costs!).  this is pretty easy to demonstrate to a business.  The other intangible effect of reducing defectives is to increase the capacity of the organization WHILE reducing the costs.  So any capacity constrained company gets HUGE benefits through reduction of defectives.

The roadblock I’ve encountered is the "quality experts" have been traditionally trained on defect recognition not defect prevention and thus see defect prevention as a threat to their livelihood.  Changing the knowledge base and culture of a profession gets to be the significant challenge we face.  That the bean counters are driven by the arithmetic, it gets even harder to justify the change (see the analysis)...the math shows it's not too bad, might even be good!  getting REAL numbers for market losses (include those lawsuits [even if risk based and the magnitude is weighted by a probability of occurrence]!!) and things like market perception, goodwill to customers, all those intangibles that affect(effect?) a buying decision get to be important.

The intuition for detecting .1% defective: pretty darn close to 0.

 Analysis:

1,000,000 produced

900,000 good

100,000 truly defective

90,000 detected defective

45,000 detected defective and really good

855,000 sold (10,000 of which are truly bad)

gross profit : 855,000-$2(10,000) = $835,000

pending scrap:135,000 units

reinspection: 51367 found good and sold: +~$51k to the $835 (~9,000 actually bad!)

still bad 83633 (not much different than the original 90K is it??) = $~63k

bad released to market ~9k = -$18k from the total

total after 200% inspection: $835 +51 - 63 -18 = ~$805k, from the ~$744 of only 100% inspection

presented this way:  200% inspection LOOKS good for the business to the tune of about $65k

add inspection costs: 1,000,000 * $.05 for first pass + 135,000 *$.05 for 2nd pass = ~$57k... still looks "not bad" as $57 looks less than $65....