findH {surveillance}R Documentation

Find decision interval for given in-control ARL and reference value

Description

Function to find a decision interval h* for given reference value k and desired ARL gamma so that the average run length for a Poisson or Binomial CUSUM with in-control parameter theta_0, reference value k and is approximately gamma, i.e. Big| frac{ARL(h^*) -gamma}{gamma} Big| < ε, or larger, i.e. ARL(h^*) > gamma .

Usage

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 gamma
theta0 in-control parameter theta_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^*) -gamma}{gamma} 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{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:

theta_1 = λ_0 + s sqrt{λ_0}

for a Poisson variate X sim Po(λ)

theta_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) -gamma}{gamma} Big|

[Package surveillance version 1.1-2 Index]