| Title: | Estimate Sample Size to Detect Bacterial Contamination in a Product Lot |
|---|---|
| Description: | Estimates the sample size needed to detect microbial contamination in a lot with a user-specified detection probability and user-specified analytical sensitivity. Various patterns of microbial contamination are accounted for: homogeneous (Poisson), heterogeneous (Poisson-Gamma) or localized(Zero-inflated Poisson). Ida Jongenburger et al. (2010) <doi:10.1016/j.foodcont.2012.02.004> "Impact of microbial distributions on food safety". Leroy Simon (1963) <doi:10.1017/S0515036100001975> "Casualty Actuarial Society - The Negative Binomial and Poisson Distributions Compared". |
| Authors: | Martine Ferguson [aut, cre]
|
| Maintainer: | Martine Ferguson <[email protected]> |
| License: | Unlimited |
| Version: | 1.0.0 |
| Built: | 2025-03-07 04:03:46 UTC |
| Source: | https://github.com/cran/msamp |
The n() function calculates the sample size,n, necessary to detect contamination above a target level, G, in a product lot, where the probability of a single sample unit being above the target level is calculated by the msamp function p(). The total cost, cost_tot, associated with sample size is also output.
n( C, w, G, Sens, D = c("homogeneous", "heterogeneous", "localized"), r = NULL, f = NULL, prob_det = 0.9, samp_dollar, lot_dollar )n( C, w, G, Sens, D = c("homogeneous", "heterogeneous", "localized"), r = NULL, f = NULL, prob_det = 0.9, samp_dollar, lot_dollar )
C |
suspected lot contamination (CFU/g) |
w |
weight of single sample unit (g) |
G |
target value to detect (CFU/g) |
Sens |
sensitivity of the analytical test (%) |
D |
distribution of the bacteria in the product lot: "homogeneous", "heterogeneous", or "localized" |
r |
for the heterogeneous case only, the degree of heterogeneity. r > 0 |
f |
for the localized case, r is further specified. 0 < f < 1 |
prob_det |
desired probability of detecting bacterial contamination above the target level in the product lot. Set to 0.9 by default |
samp_dollar |
cost per sample unit in $ |
lot_dollar |
fixed cost (if any) of sampling the lot in $ |
Refer to vignette for details.
A list containing:
n: The sample size
p: The probability of a single sample unit being contaminated above the target level
cost_tot: The total cost associated with sampling of n samples
#A sample of 25 grams (w=25) is collected and analyzed using an analytical #test with sensitivity of 90% (Sens=.9), to detect at least 5 CFU's/g (G=5). #The suspected or postulated level of contamination in the lot is 4 CFU's/g (C=4). #The desired probability of picking at least one sample unit contaminated above the target #level is 0.9 (prob_det=0.9), the cost of a single sampling unit is $100 (samp_dollar=100), #and the fixed cost for sampling the entire lot is $200 (lot_dollar=200). #homogeneous case n(C=4,w=25,G=5,Sens=.9,D="homogeneous",r=NULL,f=NULL,prob_det=0.9,samp_dollar=100,lot_dollar=200) # n=376, total cost=$37,722 #heterogeneous case n(C=4,w=25,G=5,Sens=.9,D="heterogeneous",r=10,f=NULL,prob_det=0.9,samp_dollar=100,lot_dollar=200) # n=12, total cost=$1,319 #localized case n(C=4,w=25,G=5,Sens=.9,D="localized",r=NULL,f=.3,prob_det=0.9,samp_dollar=100,lot_dollar=200) # n=1,254 , total cost=$125,541#A sample of 25 grams (w=25) is collected and analyzed using an analytical #test with sensitivity of 90% (Sens=.9), to detect at least 5 CFU's/g (G=5). #The suspected or postulated level of contamination in the lot is 4 CFU's/g (C=4). #The desired probability of picking at least one sample unit contaminated above the target #level is 0.9 (prob_det=0.9), the cost of a single sampling unit is $100 (samp_dollar=100), #and the fixed cost for sampling the entire lot is $200 (lot_dollar=200). #homogeneous case n(C=4,w=25,G=5,Sens=.9,D="homogeneous",r=NULL,f=NULL,prob_det=0.9,samp_dollar=100,lot_dollar=200) # n=376, total cost=$37,722 #heterogeneous case n(C=4,w=25,G=5,Sens=.9,D="heterogeneous",r=10,f=NULL,prob_det=0.9,samp_dollar=100,lot_dollar=200) # n=12, total cost=$1,319 #localized case n(C=4,w=25,G=5,Sens=.9,D="localized",r=NULL,f=.3,prob_det=0.9,samp_dollar=100,lot_dollar=200) # n=1,254 , total cost=$125,541
The p() function calculates the probability of a single sample unit, with weight w, and postulated contamination, C, being contaminated above a target level, G.
p( C, w, G, Sens, D = c("homogeneous", "heterogeneous", "localized"), r = NULL, f = NULL )p( C, w, G, Sens, D = c("homogeneous", "heterogeneous", "localized"), r = NULL, f = NULL )
C |
suspected lot contamination (CFU/g) |
w |
weight of single sample unit (g) |
G |
target value to detect (CFU/g) |
Sens |
sensitivity of the analytical test (%) |
D |
distribution of the bacteria in the product lot: "homogeneous", "heterogeneous", or "localized" |
r |
for the heterogeneous case only, the degree of heterogeneity. r > 0 |
f |
for the localized case, r is further specified. 0 < f < 1 |
Refer to vignette for details.
A numeric value: the probability of a single sample unit being contaminated above target level.
#A sample of 25 grams (w=25) is collected and analyzed using an analytical #test with sensitivity of 90% (Sens=.9), to detect at least 5 CFU's/g (G=5). #The suspected or postulated level of contamination in the lot is 4 CFU's/g (C=4) #homogeneous case p(C=4,w=25,G=5,Sens=.9,D="homogeneous",r=NULL,f=NULL) # 0.006117884 #heterogeneous case-- dispersion, r, is postulated as 2 p(C=4,w=25,G=5,Sens=.9,D="heterogeneous",r=2,f=NULL) # 0.2576463 #localized case -- 30% of the lot is postulated to be contaminated p(C=4,w=25,G=5,Sens=.9,D="localized",r=NULL,f=.3) # 0.001835365#A sample of 25 grams (w=25) is collected and analyzed using an analytical #test with sensitivity of 90% (Sens=.9), to detect at least 5 CFU's/g (G=5). #The suspected or postulated level of contamination in the lot is 4 CFU's/g (C=4) #homogeneous case p(C=4,w=25,G=5,Sens=.9,D="homogeneous",r=NULL,f=NULL) # 0.006117884 #heterogeneous case-- dispersion, r, is postulated as 2 p(C=4,w=25,G=5,Sens=.9,D="heterogeneous",r=2,f=NULL) # 0.2576463 #localized case -- 30% of the lot is postulated to be contaminated p(C=4,w=25,G=5,Sens=.9,D="localized",r=NULL,f=.3) # 0.001835365
The plotn() function examines the effect of increasing the probability of detection on the sample size, n, where the probability of a single sample unit being contaminated above the target limit is calculated from the msamp function p()
plotn( C, w, G, Sens, D = c("homogeneous", "heterogeneous", "localized"), r = NULL, f = NULL )plotn( C, w, G, Sens, D = c("homogeneous", "heterogeneous", "localized"), r = NULL, f = NULL )
C |
suspected lot contamination (CFU/g) |
w |
weight of single sample unit (g) |
G |
target value to detect (CFU/g) |
Sens |
sensitivity of the analytical test (%) |
D |
distribution of the bacteria in the product lot: "homogeneous", "heterogeneous", or "localized" |
r |
for the heterogeneous case only, the degree of heterogeneity. r > 0 |
f |
for the localized case, r is further specified. 0 < f < 1 |
Refer to vignette for details.
A plot, of recordedplot class. The probability of detection is on the y-axis and the sample size n is on the x-axis. Overlaid at intersecting red dashed lines is the sample size for probability of detection (prob_det) = 0.9.