Calculation of Average Run Length for discrete CUSUM schemes
arlCusum.Rd
Calculates the average run length (ARL) for an upward CUSUM scheme for discrete distributions (i.e. Poisson and binomial) using the Markov chain approach.
Usage
arlCusum(h=10, k=3, theta=2.4, distr=c("poisson","binomial"),
W=NULL, digits=1, ...)
Arguments
- h
decision interval
- k
reference value
- theta
distribution parameter for the cumulative distribution function (cdf) \(F\), i.e. rate \(\lambda\) for Poisson variates or probability \(p\) for binomial variates
- distr
"poisson"
or"binomial"
- W
Winsorizing value
W
for a robust CUSUM, to get a nonrobust CUSUM setW
>k
+h
. IfNULL
, a nonrobust CUSUM is used.- digits
k
andh
are rounded todigits
decimal places- ...
further arguments for the distribution function, i.e. number of trials
n
for binomial cdf
Value
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.
- ARL
one-sided ARL of the regular (zero-start) CUSUM scheme
- FIR.ARL
one-sided ARL of the FIR CUSUM scheme with head start \(\frac{\code{h}}{2}\)