findH {surveillance} | R Documentation |
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 .
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, ...)
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 |
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)
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| |