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

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

prob_detection_heterogeneous_multiple(mu, sd, a, b, f, u, USL, n_sim)

Arguments

mu

the mean concentration (on the log scale).

sd

the standard deviation of the normal distribution (on the log scale).

a

lower domain of the number of cell counts.

b

upper domain of the number of cell counts.

f

vector of final dilution factor.

u

vector of 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 samples collected from a heterogeneous batch.

Details

prob_detection_heterogeneous_multiple provides a probability of detection when diluted samples are collected from a heterogeneous batch. 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 heterogeneous case, we employed truncated Poisson lognormal distribution to the model. (this section will be updated later on).

Examples

mu <- 7
sd <- 0.2
a <- 0
b <- 300
f <- c(0.01,0.1,1)
u <- c(0.1,0.1,0.1)
USL <- 1000
n_sim <- 50
prob_detection_heterogeneous_multiple(mu, sd, a, b, f, u, USL, n_sim)
#>          [,1]    [,2]    [,3]
#> [1,]  0.45574 0.53556 0.65254