Dear Wayne,
It seems likely that current interest would be on a detect / non-detect procedure.
The typical 2class plan, (using a c =0 criterion) at its most stringent (ICMSF) requires (60x25g) samples / lot.
The 'false negative' is I guess (not a statistician) equivalent to the plan's characteristic which states that with 95% probability, application of such a plan would reject 19 out of 20 lots containing 2 Salmonellae cells per kg. Increased strictness will require a larger unit sample size and / or more samples. ( another viewpoint is that a -ve detection result gives an approx. 95% probability that the lot contains not more than 5% of contaminated units).
If you want to know what a -ve MPN result means, can try
http://www.cfsan.fda...bam/bam-a2.htmlnote - above link not working, an approximate replacement although perhaps condensed is -
http://www.fda.gov/F...M/ucm109656.htm(added 19-01-2010 plus the "quoted"paragraphs below)
Mathematically, zero positives has posed a difficulty in that the MPN equation is not specifically solvable. Hence comments as in above link -
'the outcome with all negative tubes is listed as less than the lowest MPN for an outcome with at least one positive tube.'
Unfortunately, this option has it's own theoretical / practical problems , eg
Prior to this revision, the 8th edition tables showed the MPN for the (0,0,0) outcomes as less than the MPN of the (1,0,0) outcome. This made good numerical sense, but made for unacceptable complexity in trying to write acceptance standards for raw materials in terms of the BAM. This revision returns to the prior practice of recording the MPN for the (0,0,0) outcomes as less than the MPN for the (0,0,1) outcome, so that standards can once again be written in a simple manner in terms of all-negative outcomes.
The above is reasonably understandable, the following reference paragraph is much less so, to me anyway, but probably is irrelevant for practical users. i enclose it just to demonstrate the complexity.
Since no particular density is indicated for an outcome of (0.0.0), a density must be assigned arbitrarily (and stated explicitly in the report) in order to calculate statistics. For the logarithm of the density, log[0.5*MPN(1,0,0)] is a reasonable choice. For statistics using the (non-logarithmic) density itself, calculate once with a density of 0.0 and once with a density of 0.5*MPN(1,0,0). Either report both statistics or report one statistic accompanied by a comment on the difference between that statistic and the other one.
http://intra.fb.uner...ium/Chapt10.htmAll this typically leads to the usual indicator expression for decision-making problems, eg -
"The 95% CI reflects the range of uncertainty as usual"
Rgds / Charles.C