Probability of detection estimation when diluted sample collected from a heterogeneous batch.

prob_detection_heterogeneous provides a probability of detection in the original sample when samples collected from a heterogeneous batch.

prob_detection_heterogeneous(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

final dilution factor.

u

amount put on the plate.

USL

upper specification limit.

n_sim

number of simulations (large simulations provide a more precise estimation).

Value

Probability of detection when sample collected from a heterogeneous batch.

Details

prob_detection_heterogeneous provides a probability of detection when the diluted sample has heterogeneous 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 heterogeneous case, we employed truncated Poisson lognormal distribution to model (this section will be updated later on).

Examples

mu <- 2
sd <- 0.2
a <- 0
b <- 300
f <- 0.01
u <- 0.1
USL <- 1000
n_sim <- 50000
prob_detection_heterogeneous(mu, sd, a, b, f, u, USL, n_sim)
#> [1] 0.00376