prob_accept {grabsampling} | R Documentation |
Probability of acceptance for grab sampling scheme
Description
This function calculates the overall probability of acceptance for given microbiological distribution such as lognormal.
Usage
prob_accept(c, r, t, mu, distribution, K, m, sd)
Arguments
c |
acceptance number |
r |
number of primary increments in a grab sample or grab sample size |
t |
number of grab samples |
mu |
location parameter (mean log) of the Lognormal and Poisson-lognormal distributions on the log10 scale |
distribution |
what suitable microbiological distribution we have used such as |
K |
dispersion parameter of the Poisson gamma distribution (default value 0.25) |
m |
microbiological limit with default value zero, generally expressed as number of microorganisms in specific sample weight |
sd |
standard deviation of the lognormal and Poisson-lognormal distributions on the log10 scale (default value 0.8) |
Details
Based on the food safety literature, for given values of c
, r
and t
, the probability of detection in a primary increment is given by, and acceptance probability in
t
selected sample is given by .
If Y be the sum of correlated and identically distributed lognormal random variables X, then the approximate distribution of Y is lognormal
distribution with mean , standard deviation
(see Mehta et al (2006)) where
and
for all
.
The parameters and
of the grab sample unit Y is given by,
(see Mussida et al (2013)). For this package development, we have used fixed value with default value 0.8.
Value
Probability of acceptance
References
Mussida, A., Vose, D. & Butler, F. Efficiency of the sampling plan for Cronobacter spp. assuming a Poisson lognormal distribution of the bacteria in powder infant formula and the implications of assuming a fixed within and between-lot variability, Food Control, Elsevier, 2013 , 33 , 174-185.
Mehta, N.B, Molisch, A.F, Wu, J, & Zhang, J., 'Approximating the Sum of Correlated Lognormal or, Lognormal-Rice Random Variables,' 2006 IEEE International Conference on Communications, Istanbul, 2006, pp. 1605-1610.
Examples
c <- 0
r <- 25
t <- 30
mu <- -3
distribution <- 'Poisson lognormal'
prob_accept(c, r, t, mu, distribution)