True concentration level estimation when diluted sample collected from a homogeneous batch. — true_concentration

These functions provides true concentration level in the original sample when diluted samples collected from a homogeneous batch.

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

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

true_concentration_curves_homogeneous(lambda_low, lambda_high, 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 a more precise estimation).
lambda_low: the lower value of the expected cell count ($\lambda$) for use in the graphical display's x-axis.
lambda_high: the upper value of the expected cell count ($\lambda$) for use in the graphical display's x-axis.

Value

true concentration level when the diluted sample collected from a homogeneous batch.

Details

Let Y be the count of microorganisms and C be the true concentration level (in counts per ml). When diluted sample collected from homogeneous batch, Y can be modelled by Poisson distribution with parameter $\lambda$. Let X be the count of microorganisms on a plate, and it can be modelled by truncated Poisson distribution with parameters $\lambda_d, a, b$. Also, $\lambda_d$ can be written in terms of $\lambda$,f and u. It is given by $$\lambda_d = \lambda * f *u$$ And the true concentration level is given by $$C = \frac{X}{f*u}$$

Examples

lambda_low <- 1
lambda_high <- 10000
a <- 0
b <- 300
f <- c(0.01,0.1)
u <- c(0.1,0.1)
USL <- 1000
n_sim <- 20000
true_concentration_curves_homogeneous(lambda_low, lambda_high, a, b, f, u, USL, n_sim)