Probability of detection estimation for multiple dilution schemes when diluted samples are collected from a homogeneous batch.

prob_detection_homogeneous_multiple provides a probability of detection for multiple dilution schemes in the original sample when samples collected from a homogeneous batch.

prob_detection_homogeneous_multiple(lambda, a, b, f, u, USL, n_sim)

Arguments

lambda

the expected cell count (\(\lambda\)).

a

lower domain of the number of cell counts.

b

upper domain of the number of cell counts.

f

final dilution factor.

u

amount put on the plate.

USL

upper specification limit.

n_sim

number of simulations (large simulations provide more precise estimations).

Value

Probability of detection when diluted samples are collected from a homogeneous batch.

Details

prob_detection_homogeneous_multiple provides a probability of detection when the diluted sample has homogeneous contaminants. We define the random variable \(X_{i}\) is the number of colonies on the \(i^{th}\) plate. In practice, the acceptance for countable numbers of colonies on a plate must be between 30 and 300. Therefore, we can utilise bounded distributions to model the number of colonies on a plate. In the homogeneous case, we employed truncated Poisson distribution to model (this section will be updated later on).

Examples

lambda <- 1000
a <- 0
b <- 300
f <- c(0.01,0.1,1)
u <- c(0.1,0.1,0.1)
USL <- 1000
n_sim <- 50000
prob_detection_homogeneous_multiple(lambda, a, b, f, u, USL, n_sim)
#>         [,1]    [,2]    [,3]
#> [1,] 0.41828 0.41822 0.47332