Calculates the average run length (ARL) for an upward CUSUM scheme for discrete distributions (i.e. Poisson and binomial) using the Markov chain approach.
arlCusum(h=10, k=3, theta=2.4, distr=c("poisson","binomial"),
W=NULL, digits=1, ...)
Returns a list with the ARL of the regular (zero-start)
and the fast initial response (FIR)
CUSUM scheme with reference value k
, decision interval h
for
\(X \sim F(\theta)\), where F is the Poisson or binomial CDF.
one-sided ARL of the regular (zero-start) CUSUM scheme
one-sided ARL of the FIR CUSUM scheme with head start \(\frac{\code{h}}{2}\)
decision interval
reference value
distribution parameter for the cumulative distribution function (cdf) \(F\), i.e. rate \(\lambda\) for Poisson variates or probability \(p\) for binomial variates
"poisson"
or "binomial"
Winsorizing value W
for a robust CUSUM,
to get a nonrobust CUSUM set
W
> k
+h
. If NULL
, a nonrobust CUSUM is used.
k
and h
are rounded to digits
decimal places
further arguments for the distribution function, i.e. number of trials n
for binomial cdf