1
Principles of microbiological Principles of microbiological testing: Statistical basis of testing: Statistical basis of
samplingsampling
Martin ColeSymposium on Relating Microbiological Testing and Microbiological Criteria to Public Health GoalsOctober 31-November 1, 2005
OverviewOverview
Sampling plansSampling plansICMSF CasesICMSF CasesStatistical basisStatistical basisPerformance of sampling plansPerformance of sampling plansSummary and ConclusionsSummary and Conclusions
2
Sampling PlansSampling Plans
Define the probability of Define the probability of detecting a microorganisms or detecting a microorganisms or other hazards in a lotother hazards in a lotNone can ensure the absence of a None can ensure the absence of a particular hazardparticular hazardShould be administratively and Should be administratively and economically feasibleeconomically feasible
Types of Microbiological Types of Microbiological Sampling PlansSampling Plans
Attributes plans:
Qualitative analytical results (presence/absence) orquantitative results that have been grouped(e.g. <10 cfu/g, 10 to 100 cfu/g, >100 cfu/g)
Variables plans:
Non-grouped quantitative analytical results
Require distributional assumptions be made
3
TwoTwo--Class Attributes Class Attributes Sampling PlansSampling Plans
TwoTwo--class sampling plansclass sampling plans designed to decide designed to decide on acceptance or rejection of a lot consist ofon acceptance or rejection of a lot consist of
nn –– number of sample units to be chosen number of sample units to be chosen independently and randomly from the lotindependently and randomly from the lotmm –– a microbiological limit (i.e. in cfu/g);a microbiological limit (i.e. in cfu/g);a sample is defined to be positive, if its a sample is defined to be positive, if its microbial content exceeds this limitmicrobial content exceeds this limitcc –– maximum allowable number of sample maximum allowable number of sample units yielding a positive result units yielding a positive result (presence/absence testing) or exceeding the (presence/absence testing) or exceeding the microbiological limit m; for pathogens c is microbiological limit m; for pathogens c is usually set to 0usually set to 0
Log cfu/g
Pro
babi
lity
Den
sity
0 1 2 3 4 5 6
0.0
0.1
0.2
0.3
0.4
0.5
0.6m
Proportion defective
Two-class sampling plan:
4
OC Curve for TwoOC Curve for Two--Class Class PlansPlans
Operation characteristics (OC) or performance for two-class sampling plans:
Probability of lot acceptance calculated for possible proportions defective in lot
Plot of OC curve to visualize
sampling plan performance
dependency on n and c
Proportion defectiveA
ccep
tanc
e pr
obab
ility
Proportion Defective
Pro
babi
lity
of A
ccep
tanc
e
0.0 0.2 0.4 0.6 0.8
0.0
0.2
0.4
0.6
0.8
1.0
P(acceptance)
P(rejection)
Probability of Acceptance by Proportion Defective
n=5, c=0
5
Proportion Defective
Prob
abilit
y of
Acc
epta
nce
0.0 0.2 0.4 0.6 0.8
0.0
0.2
0.4
0.6
0.8
1.0
P(acceptance)
P(rejection)
Probability of Acceptance by Proportion Defective
n=5, c=0
Consumer’s risk‘Probability of accepting A defective lot’
Producer’s risk‘Probability that anacceptable lot is rejected’
ThreeThree--Class Attributes Class Attributes Sampling PlansSampling Plans
ThreeThree--class sampling plansclass sampling plans consist ofconsist ofnn –– number of sample units to be chosen number of sample units to be chosen independently and randomly from the lotindependently and randomly from the lotmm –– a microbiological limit that separates a microbiological limit that separates good quality from marginally acceptable good quality from marginally acceptable quality quality MM –– a microbiological limit above which a microbiological limit above which sampling results are unacceptable or sampling results are unacceptable or defectivedefectivecc –– maximum allowable number of sample maximum allowable number of sample unitsunitsyielding results between m and M yielding results between m and M (marginally acceptable);(marginally acceptable);the number of sample units allowed to the number of sample units allowed to exceed M is usually set to 0 exceed M is usually set to 0
6
Log cfu/g
Prob
abilit
y D
ensi
ty
0 1 2 3 4 5 6
0.0
0.1
0.2
0.3
0.4
0.5
0.6m M
Proportion defective
Proportion marginally acceptable
Three-class sampling plan:
OC Function for ThreeOC Function for Three--Class Class PlansPlans
Operation characteristics (OC) or performance for three-class plans:
Probability of lot acceptance depending on two proportions
marginally acceptable: between m and M
defective: above M
OC function plotted as a three-dimensional graph A
ccep
tanc
e pr
obab
ility
Proportion defective
Prop. marginally acceptable
7
Operating Characteristic Curves, 3-Class Plans
P(acc)
ICMSF CasesICMSF Cases
15 cases which reflect:15 cases which reflect:Degree of riskDegree of riskConditions of useConditions of useIntended PopulationIntended Population
8
Risk categorization matrixRisk categorization matrix
Food handling conditionsFood handling conditionsa b ca b c
AAHealthHealthhazardhazard BB
CC
increasedrisk
A) ModerateA) Moderate::
B) SeriousB) Serious::
C) SevereC) Severe: :
S. aureus toxinV. parahaemolyticusB. cereusEPEC
Salmonella (non typhi)ShigellaListeria monocytogenes
EHEC (STEC, VTEC)V. cholerae O1EPEC for infants
Categories of hazardsCategories of hazards
9
Plan Stringency (Case) in Relation to Degree of Plan Stringency (Case) in Relation to Degree of Health Concern and Conditions of Use.Health Concern and Conditions of Use.
Type of Hazard Reduce Degreeof Hazard
Cause No Changein Hazard
May IncreaseHazard
No direct healthhazard
Utility (generalcontamination)
Case 1 Case 2 Case 3
Health HazardLow, indirect(indicator)
Case 4 Case 5 Case 6
Moderate, direct,limited spread
Case 7 Case 8 Case 9
Moderate, direct,potentiallyextensive spread
Case 10 Case 11 Case 12
Severe, direct Case 13 Case 14 Case 15
TwoTwo--Class Plans (c=0): Probabilities of AcceptanceClass Plans (c=0): Probabilities of Acceptance
Composition of Lot% Acceptable % Defective
Number of Sample Units Tested5 10 20 60 100
98
95
90
80
70
50
40
30
2
5
10
20
30
50
60
70
.90
.77
.59
.17
.03
.01
<
.82
.60
.35
.11
.03
<
.67
.36
.12
.01
<
.30
.05
<
.13
.01
<
Typical way of expressing performance of sampling plans
10
Important Properties of Sampling
Gonick & Smith, Harper Resource, 1993.
Microbial Sampling is a Bernoulli Trial
Gonick & Smith, Harper Resource, 1993.
11
Operating Characteristic Curve
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Proportion Defective
Prob
abili
ty o
f acc
epta
nce
n=0
Operating Characteristic Curve
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Proportion Defective
Prob
abili
ty o
f acc
epta
nce
n=1Example:
0.1 Proportion Defective
Probability of Acceptance =
0.9 = 0.9
12
Operating Characteristic Curve
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Proportion Defective
Prob
abili
ty o
f acc
epta
nce
n=2Example:
0.1 Proportion Defective
Probability of Acceptance =
0.9 x 0.9 = 0.81
Operating Characteristic Curve
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Proportion Defective
Prob
abili
ty o
f acc
epta
nce
n=3Example:
0.1 Proportion Defective
Probability of Acceptance =
0.9 x 0.9 x 0.9 = 0.73
13
Operating Characteristic Curve
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Proportion Defective
Prob
abili
ty o
f acc
epta
nce
n=4
Example:
0.1 Proportion Defective
Probability of Acceptance =
0.9 x 0.9 x 0.9 x 0.9= 0.66
Operating Characteristic Curve
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Proportion Defective
Prob
abili
ty o
f acc
epta
nce
n = 5Example:
0.1 Proportion Defective
Probability of Acceptance =
0.9 x 0.9 x 0.9 x 0.9 x 0.9 = 0.59
14
Operating Characteristic Curve
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Proportion Defective
Prob
abili
ty o
f acc
epta
nce
n = 10
Operating Characteristic Curve
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Proportion Defective
Prob
abili
ty o
f acc
epta
nce
n = 20
15
Operating Characteristic Curve
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Proportion Defective
Prob
abili
ty o
f acc
epta
nce
n = 30
Operating Characteristic Curve
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Proportion Defective
Prob
abili
ty o
f acc
epta
nce
‘Idealized’ Situation
P(acc) =0P(rej) = 1
P(acc) =1P(rej) = 0
16
Operating Characteristic Curve
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Proportion Defective
Prob
abili
ty o
f acc
epta
nce
n = 5Example: 0.1 Proportion DefectiveProbability of Acceptance = 0.9 x 0.9 x 0.9 x 0.9 x 0.9 = 0.59
c = 10.1 x 0.9 x 0.9 x 0.9 x 0.9 = 0.0650.9 x 0.1 x 0.9 x 0.9 x 0.9 = 0.0650.9 x 0.9 x 0.1 x 0.9 x 0.9 = 0.0650.9 x 0.9 x 0.9 x 0.1 x 0.9 = 0.0650.9 x 0.9 x 0.9 x 0.9 x 0.1 = 0.065i.e. 5 ways = 0.329
So probability of accepting lot is 0.59 + 0.329 = 0.918
Performance of sampling plansPerformance of sampling plansand concentration controlledand concentration controlled
Alternative approach for quantitative data:
Distributional assumption for sampling resultse.g. log-normal with standard deviation known fromprevious experience
Determine proportions acceptable, (marginally acceptable), and defectivefor possible mean log cfu/g
Calculate acceptance probabilities and plot against mean log cfu/g
17
Gonick & Smith, Harper Resource, 1993.
‘When the error is proportional to the measurement the use of logarithms is likely to produce normal curves……’
Gaddum, Nature No.3964, October 20, 1945
18
Log Normality of Total Viable Counts in Log Normality of Total Viable Counts in Batches of FoodsBatches of Foods
7.87.81281128110010066OverallOverall
12.712.7118118151522PowderedPowdered
9.69.652525511Frozen dairyFrozen dairy
2.42.441411111Frozen Frozen vegveg
8.28.2159159131322Frozen meatFrozen meat
7.97.9393393313111Frozen Frozen crust.crust.
6.76.7518518353522Frozen fishFrozen fish
% of % of batchesbatchesNOT LOGNOT LOGNORMALNORMAL
No. of No. of batchesbatchesExaminedExamined
No. of No. of batches batches NOT LOGNOT LOGNORMALNORMAL
No. ofNo. ofSuppliersSuppliers
CommodityCommodity
Fillibens (1975), Techometrics, 17, 111-117
Campylobacter jejuni/coli in raw ground chicken-source Nationwide Raw Chicken Micro.survey,
Mar 1995-May1995 mean=0, sigma =0.8
0.00
0.20
0.40
0.60
0.80
1.00
-6.0 -5.0 -4.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 5.0 6.0
Log MPN/g
Prob
abili
ty
Distribution
AccumulatedDistributionActual Values
19
APC in raw ground chicken-source Nationwide Raw Chicken Micro.survey, Mar 1995-May1995
mean=4.5, sigma =0.8
0.00
0.20
0.40
0.60
0.80
1.00
-6.0 -5.0 -4.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 5.0 6.0
Log MPN/g
Prob
abili
ty
Distribution
AccumulatedDistributionActual Values
Assumed Distribution of Enterbacter sakazakii in PIF based on all available published data
mean=-4.0, sigma =.8
0.000.200.400.600.801.00
-6.0 -5.0 -4.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 5.0 6.0
Log MPN/g
Prob
abili
ty
Distribution
AccumulatedDistributionActual Values
20
Prob
abili
ty D
ensi
ty
Log cfu/g
m
0.0 1.0 2.0 3.0 4.0 5.0 6.0
Linking the Performance of attribute sampling plans to the concentration of bacteria controlled
m
pa
0.0 1.0 2.0 3.0 4.0 5.0 6.0
Prob
abili
ty D
ensi
ty
Log cfu/g
Proportion Defective
21
0.0 1.0 2.0 3.0 4.0 5.0 6.0
m
pa
Prob
abili
ty D
ensi
ty
Log cfu/g
0.0 1.0 2.0 3.0 4.0 5.0 6.0
m
pa pd
Prob
abili
ty D
ensi
ty
Log cfu/g
22
0.0 1.0 2.0 3.0 4.0 5.0 6.0
m
pa pd
Prob
abili
ty D
ensi
ty
Log cfu/g
0.0 1.0 2.0 3.0 4.0 5.0 6.0
m
pa pd
Prob
abili
ty D
ensi
ty
Log cfu/g
23
0.0 1.0 2.0 3.0 4.0 5.0 6.0
m
pdpa
Prob
abili
ty D
ensi
ty
Log cfu/g
0.0 1.0 2.0 3.0 4.0 5.0 6.0
m
pa pd
Prob
abili
ty D
ensi
ty
Log cfu/g
24
0.0 1.0 2.0 3.0 4.0 5.0 6.0
m
pd
Prob
abili
ty D
ensi
ty
Log cfu/g
0.0 1.0 2.0 3.0 4.0 5.0 6.0
m
pd
Prob
abili
ty D
ensi
ty
Log cfu/g
25
0.0 1.0 2.0 3.0 4.0 5.0 6.0
mPr
obab
ility
Den
sity
Log cfu/g
Mean Log cfu/g
0.0
0.2
0.4
0.6
0.8
1.0
Prop
ortio
n de
fect
ive,
pd
m
26
0.0
0.2
0.4
0.6
0.8
1.0
Prop
ortio
n de
fect
ive,
pd
Mean Log cfu/g
m
0.0
0.2
0.4
0.6
0.8
1.0
m
Prop
ortio
n de
fect
ive,
pd
Mean Log cfu/g
27
0.0
0.2
0.4
0.6
0.8
1.0
Prop
ortio
n de
fect
ive,
pd
Mean Log cfu/g
m
0.0
0.2
0.4
0.6
0.8
1.0
m
Prop
ortio
n de
fect
ive,
pd
Mean Log cfu/g
28
0.0
0.2
0.4
0.6
0.8
1.0
m
Prop
ortio
n de
fect
ive,
pd
Mean Log cfu/g
0.0
0.2
0.4
0.6
0.8
1.0
m
Prop
ortio
n de
fect
ive,
pd
Mean Log cfu/g
29
0.0
0.2
0.4
0.6
0.8
1.0
m
Prop
ortio
n de
fect
ive,
pd
Mean Log cfu/g
0.0
0.2
0.4
0.6
0.8
1.0
Prop
ortio
n de
fect
ive,
pd
Mean Log cfu/g
m
30
0.0
0.2
0.4
0.6
0.8
1.0
m
Prop
ortio
n de
fect
ive,
pd
Mean Log cfu/g
0.0
0.2
0.4
0.6
0.8
1.0
m
Prop
ortio
n de
fect
ive,
pd
Mean Log cfu/g
31
0.00.20.40.60.81.0
p d
pd
P(ac
cept
)
OC curven = 10,c = 2
1.0
0.0
0.2
0.4
0.6
0.8
Mean log cfu/g
Prob
abili
ty o
f acc
epta
nce
0.00.20.40.60.81.0
p d
pd
P(ac
cept
)
OC curven = 10,c = 2
1.0
0.0
0.2
0.4
0.6
0.8
Mean log cfu/g
Prob
abili
ty o
f acc
epta
nce
32
0.00.20.40.60.81.0
p d
pdP(
acce
pt)
OC curven = 10,c = 2
1.0
0.0
0.2
0.4
0.6
0.8
Mean log cfu/g
Prob
abili
ty o
f acc
epta
nce
0.00.20.40.60.81.0
p d
pd
P(ac
cept
)
OC curven = 10,c = 2
1.0
0.0
0.2
0.4
0.6
0.8
Mean log cfu/g
Prob
abili
ty o
f acc
epta
nce
33
0.00.20.40.60.81.0
p d
pd
P(ac
cept
)
OC curven = 10,c = 2
1.0
0.0
0.2
0.4
0.6
0.8
Mean log cfu/g
Prob
abili
ty o
f acc
epta
nce
0.00.20.40.60.81.0
p d
pd
P(ac
cept
)
OC curven = 10,c = 2
1.0
0.0
0.2
0.4
0.6
0.8
Mean log cfu/g
Prob
abili
ty o
f acc
epta
nce
34
0.00.20.40.60.81.0
p d
pd
P(ac
cept
)
OC curven = 10,c = 2
1.0
0.0
0.2
0.4
0.6
0.8
Mean log cfu/g
Prob
abili
ty o
f acc
epta
nce
0.00.20.40.60.81.0
p d
pd
P(ac
cept
)
OC curven = 10,c = 2
1.0
0.0
0.2
0.4
0.6
0.8
Mean log cfu/g
Prob
abili
ty o
f acc
epta
nce
35
0.00.20.40.60.81.0
p d
pd
P(ac
cept
)
OC curven = 10,c = 2
1.0
0.0
0.2
0.4
0.6
0.8
Mean log cfu/g
Prob
abili
ty o
f acc
epta
nce
0.00.20.40.60.81.0
p d
pd
P(ac
cept
)
OC curven = 10,c = 2
1.0
0.0
0.2
0.4
0.6
0.8
Mean log cfu/g
Prob
abili
ty o
f acc
epta
nce
36
0.00.20.40.60.81.0
p d
pd
P(ac
cept
)
OC curven = 10,c = 2
1.0
0.0
0.2
0.4
0.6
0.8
Mean log cfu/g
Prob
abili
ty o
f acc
epta
nce
Performance of Sampling Performance of Sampling PlansPlans
Sampling plan stringency, steepness of OC curve, location of critical lot qualities (95% probability of rejection, 95% probability of acceptance)depend on
Plan specifications n and c
Microbiological limits m and M
Standard deviation s.d.
Difference M-m in relation to s.d.
37
0-3 -2 -1 1 2 3
1000/g100/g10/g1g1cfuin
10g
1cfuin
100g
1cfuIn1 Kg
LOG Conc.
Effect of number of samples(m=1/g, s.d. =0.8)
123510
Mean Concentration Controlled with a 95% Probability
30
0
0-3 -2 -1 1 2 3
1000/g100/g10/g1g1cfuin
10g
1cfuin
100g
1cfuIn1 Kg
LOG Conc.
Effect of limit m/sample size(n=5, s.d. =0.8)
100cfu/g10cfu/g1cfu/g
Absencein
25g
Absencein
15 x 25g
Mean Concentration Controlled with a 95% Probability
0
38
0-3 -2 -1 1 2 3
1000/g100/g10/g1g1cfuin
10g
1cfuin
100g
1cfuIn1 Kg
LOG Conc.
Effect of Standard Deviation(n=3, m = 1/g)
0.12.4
1.60.8
Mean Concentration Controlled with a 95% Probability
0
ICMSF ThreeICMSF Three--Class Plans: Mean CFU/G Class Plans: Mean CFU/G Rejected With 95% ProbabilityRejected With 95% Probability
Case 9:Case 9:n=10, c=1n=10, c=1575 cfu/g575 cfu/g
Case 8:Case 8:n=5, c=1n=5, c=11819 cfu/g1819 cfu/g
Case 7:Case 7:n=5, c=3n=5, c=33311 cfu/g3311 cfu/g
Case 6:Case 6:n=5, c=1n=5, c=11819 cfu/g1819 cfu/g
Case 5:Case 5:n=5, c=2n=5, c=23311 cfu/g3311 cfu/g
Case 4:Case 4:n=5, c=3n=5, c=35128 cfu/g5128 cfu/g
With:m = 1000 cfu/g, M = 10 000 cfu/g,and standard deviation s.d. = 0.8
39
ICMSF ThreeICMSF Three--Class Plans: Mean Class Plans: Mean Implied POs(based on mean count +3sds)Implied POs(based on mean count +3sds)
Case 9:Case 9:n=10, c=1n=10, c=1144435 144435 cfu/gcfu/g
Case 8:Case 8:n=5, c=1n=5, c=1456912 456912 cfu/gcfu/g
Case 7:Case 7:n=5, c=3n=5, c=3831685 831685 cfu/gcfu/g
Case 6:Case 6:n=5, c=1n=5, c=1456912 456912 cfu/gcfu/g
Case 5:Case 5:n=5, c=2n=5, c=2881923 881923 cfu/gcfu/g
Case 4:Case 4:n=5, c=3n=5, c=31288095 1288095 cfu/gcfu/g
With:m = 1000 cfu/g, M = 10 000 cfu/g,and standard deviation s.d. = 0.8
ICMSF TwoICMSF Two--Class Plans: Mean CFU/G Class Plans: Mean CFU/G Rejected With 95% ProbabilityRejected With 95% Probability
Case 15:Case 15:n=60, c=0n=60, c=01 cfu / 526g1 cfu / 526g
Case 14:Case 14:n=30, c=0n=30, c=01 cfu / 278g1 cfu / 278g
Case 13:Case 13:n=15, c=0n=15, c=01 cfu / 135g1 cfu / 135g
Case 12:Case 12:n=20, c=0n=20, c=01 cfu / 185g1 cfu / 185g
Case 11:Case 11:n=10, c=0n=10, c=01 cfu / 83g1 cfu / 83g
Case 10:Case 10:n=5, c=0n=5, c=01 cfu / 32g1 cfu / 32g
With:m = 0 cfu / 25g,and standard deviation s.d. = 0.8
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ICMSF TwoICMSF Two--Class Plans: Class Plans: Implied PO (based on mean count +3sds)Implied PO (based on mean count +3sds)
Case 15:Case 15:n=60, c=0n=60, c=00.4cfu/g0.4cfu/g
Case 14:Case 14:n=30, c=0n=30, c=00.9cfu/g0.9cfu/g
Case 13:Case 13:n=15, c=0n=15, c=01.85cfu/g1.85cfu/g
Case 12:Case 12:n=20, c=0n=20, c=01.25cfu/g1.25cfu/g
Case 11:Case 11:n=10, c=0n=10, c=02.5cfu/g2.5cfu/g
Case 10:Case 10:n=5, c=0n=5, c=07.7cfu/g7.7cfu/g
With:m = 0 cfu / 25g,and standard deviation s.d. = 0.8
Relationship of Microbiological Relationship of Microbiological Criteria to Criteria to FSOFSO’’ss
FSOFSO: A statement of the maximum : A statement of the maximum frequency and/or concentration of a frequency and/or concentration of a microbiological hazard in a food microbiological hazard in a food considered tolerable for consumer considered tolerable for consumer protectionprotectionMicrobiological CriteriaMicrobiological Criteria: The : The acceptability of a product or a food lot, acceptability of a product or a food lot, based on the absence or presence, or based on the absence or presence, or number of microorganisms, and/or of number of microorganisms, and/or of mass, volume, area, or lot .mass, volume, area, or lot .
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Summary and ConclusionsSummary and Conclusions
No feasible sampling plan can ensure absence No feasible sampling plan can ensure absence of a pathogenof a pathogenMicrobial sampling is a Microbial sampling is a ‘‘Bernoulli trialBernoulli trial’’Stringency depends on key parametersStringency depends on key parametersPossible to link performance to mean Possible to link performance to mean concentration controlledconcentration controlled
ICMSF Sampling Plan Spreadsheetwww.icmsf.org
Acknowledgments
Resources
ICMSF members & consultantsSusanne DahmsRuss FlowersMike van SchothorstBob BuchananBruce TompkinDavid Legan