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. $\Big| \frac{ARL(h^*) -\gamma}{\gamma} \Big| < \epsilon$,
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, ...)"poisson" or "binomial"h* is
stopped if $\Big| \frac{ARL(h^*) -\gamma}{\gamma} \Big| <$ k and the decision interval h
are rounded to digits decimal placesfindKTRUE, the decision interval that leads to the desired ARL
for a FIR CUSUM with head start
$\frac{\code{h}}{2}$ is returnedn for binomial cdffindH returns a vector and hValues returns a matrix with elementsk and hk
is specified as:
$$\theta_1 = \lambda_0 + s \sqrt{\lambda_0}$$
for a Poisson variate $X \sim Po(\lambda)$$$\theta_1 = \frac{s \pi_0}{1+(s-1) \pi_0}$$ for a Binomial variate $X \sim Bin(n, \pi)$