# findH: Find decision interval for given in-control ARL and reference... In surveillance: Temporal and Spatio-Temporal Modeling and Monitoring of Epidemic Phenomena

## Description

Function to find a decision interval h* for given reference value k and desired ARL γ so that the average run length for a Poisson or Binomial CUSUM with in-control parameter θ_0, reference value k and is approximately γ, i.e. \Big| \frac{ARL(h^*) -γ}{γ} \Big| < ε, or larger, i.e. ARL(h^*) > γ .

## Usage

 1 2 3 4 5 findH(ARL0, theta0, s = 1, rel.tol = 0.03, roundK = TRUE, distr = c("poisson", "binomial"), digits = 1, FIR = FALSE, ...) hValues(theta0, ARL0, rel.tol=0.02, s = 1, roundK = TRUE, digits = 1, distr = c("poisson", "binomial"), FIR = FALSE, ...) 

## Arguments

 ARL0 desired in-control ARL γ theta0 in-control parameter θ_0 s change to detect, see details distr "poisson" or "binomial" rel.tol relative tolerance, i.e. the search for h* is stopped if \Big| \frac{ARL(h^*) -γ}{γ} \Big| < rel.tol digits the reference value k and the decision interval h are rounded to digits decimal places roundK passed to findK FIR if TRUE, the decision interval that leads to the desired ARL for a FIR CUSUM with head start \frac{\code{h}}{2} is returned ... further arguments for the distribution function, i.e. number of trials n for binomial cdf

## Details

The out-of-control parameter used to determine the reference value k is specified as:

θ_1 = λ_0 + s √{λ_0}

for a Poisson variate X \sim Po(λ)

θ_1 = \frac{s π_0}{1+(s-1) π_0}

for a Binomial variate X \sim Bin(n, π)

## Value

findH returns a vector and hValues returns a matrix with elements

 theta0 in-control parameter h decision interval k reference value ARL ARL for a CUSUM with parameters k and h rel.tol corresponds to \Big| \frac{ARL(h) -γ}{γ} \Big|

surveillance documentation built on July 25, 2018, 1:01 a.m.