# 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

## 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 \(\frac{\code{h}}{2}\)