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Conference rusure::math

Title:Mathematics at DEC
Moderator:RUSURE::EDP
Created:Mon Feb 03 1986
Last Modified:Fri Jun 06 1997
Last Successful Update:Fri Jun 06 1997
Number of topics:2083
Total number of notes:14613

1849.0. "Stats help: Sig of Diff np<5" by CARROL::COX (Ed Cox: II Cor 10:3-5) Thu Mar 03 1994 14:26

      I find myself in need of testing significance of difference between
      several pairs of attribute (defect count) data, several of which
      fall into the category of np<5.  Such low number of observed defects
      is not covered by any formula which I have found.  I have tried 
      deriving my own methodology using Mathcad, but the results so far
      produce results which intuitively too high.  Could some one point
      me in the right direction?
      - Ed
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1849.1Some quick answers.CADSYS::COOPERTopher CooperThu Mar 03 1994 16:4911
    Due to the storm, I'm coming in from home over a noisy line, so I'll
    keep this brief, and provide more info when I come into work.

    Exact tests can be developed if none of your expectations are much
    above 5.  Some modern thought says that you can tolerate some cells
    with 1<=np<5, based on simulations but the advice is "fuzzy" as to
    just when you can manage this.  A technique called a randomization test
    may solve your problem, though it makes interpretation of just what
    your "p-value" means somewhat trickier.

					Topher
1849.2Need more info.CADSYS::COOPERTopher CooperMon Mar 07 1994 18:3913
    To know what to advise, I really need to know more about your problem.
    Let me take a wild guess and you tell me where I am wrong.

    You have some product which you are manufacturing, and you have, as
    part of the specification, that the rate of defects (i.e., the
    proportion of the products which are defective) should be no more than
    "p".  You test "n" of the products of which "d" are defective, and you
    would like to be able to make a statement to the effect that you are
    99% sure that the defect rate is no more than p.

    I'm sure that that is wrong, but tell me why it is wrong.

					    Topher
1849.3CARROL::COXEd Cox: II Cor 10:3-5Thu Apr 14 1994 20:5219
The problem is related to process development in an environment in which the
the acceptable defect rate targets keep getting smaller.  This drives the
sample sizes required to establish that defect rate very large.  (Some
managerial types seem to have difficulty with why you can not prove a 10ppm
defect rate with a sample size of 1000 opportunities for defects!) In a
recent experiment (that someone else did) they supported a rather significant
process decision on a comparison of 1 defect out of 14,256 verses 4 defects
out of 14,256.  I had some other data that included more combination of
test variables which gave a more complete picture of the situation and which
had observed defect counts from the mid single digits up to several hundred
based on different sample sizes ranging from 1/2 to about 1/6 of the
14,256 sample size of the other data.  Pure intuition tells me which
data is going to be more reliable, but I would like to be able to attach
real confidence limits on the conclusions.  The 1 & 4 defects from the 
other experiment has left me scratching my head for a legitimate method
of doing this.

Does that help explain what I am looking for?
- Ed
1849.4RTL::GILBERTMon Apr 18 1994 19:457
    Instead of measuring a binary value (i.e., defect vs no defect), are
    there other, more continuous metrics available?
    
    Supposing that such a metric were used, a value outside a prescribed range
    would constitute a 'defect'.  You can fit an error curve to the measured
    values of a moderately-sized sample, and from that estimate the probability
    of a 'defect'.
1849.5CARROL::COXEd Cox: II Cor 10:3-5Wed Apr 20 1994 16:418
Believe me, looking for a continuous variable is always my first preference,
but so far no one I know of has found a substitute for counting electrical
opens and shorts on a module.  I have done some modeling of the major factors
which affect the opens and shorts on fine pitch SMT devices and it correlates
well with actual data.  This helps tremendously, but there are some factors
which I just can not figure out how to model and the only way to measure
their effects is to count defects (yuk).
- Ed