RE: Tom Ryan's reply to the SPC theory point

["DeRoeck, Rich" <RDeRoeck@alphaind.com>]

>>This is the reason C=0 sampling is the only attribute scheme accepted in
the automotive industry.<<

There is nothing special about c=0 plans. In fact many c=0 plans (with small
sample sizes) provide terrible consumer protection. The best way to
understand attribute sampling plans is by using the Operational Curves (OC)
developed by Dodge in the 1930-1940's. These curves show the probability of
acceptance (Pa) vs. the fraction non-conforming (p). The most important
variable is the absolute sample size (n). Neither the sample size as a
percentage of the lot size (N) or the acceptance number (c) is as important.


For example, let's say you receive a lot size (N) of 1000 parts from your
supplier.
  
Sampling Plan-1 uses n=13,c=0
Sampling Plan-2 uses n=50,c=1
Sampling Plan-2 uses n=80,c=2

Let's say the supplier's quality level (p) for this lot is 0.05 defective.
The probability of acceptance for the c=0 plan is approx. 51% while the Pa
for the c=1 plan is approx. 28% and the c=2 plan is approx. 22%. So which
plan provides better consumer protection? In the example above the best plan
is n=80,c=2. 

Of course, if the sample sizes were all the same the c=0 plan would be best,
but sample size is the major factor. Also, with the c=0 plans the largest
slope (drop) on the OC curve takes place  at the best quality level
(smallest p). A good reference book on this subject is: "The Handbook of
Applied Acceptance Sampling" by Ken Stephens (ASQ Press).

Rich DeRoeck
IQA Supervisor
Alpha Industries