# arlCusum: Calculation of Average Run Length for discrete CUSUM schemes

Description Usage Arguments Value Source

### Description

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

 1 2 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 λ 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 set W > k+h. If NULL, a nonrobust CUSUM is used. digits k and h are rounded to digits 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(θ), 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}

### Source

Based on the FORTRAN code of

Hawkins, D. M. (1992). Evaluation of Average Run Lengths of Cumulative Sum Charts for an Arbitrary Data Distribution. Communications in Statistics - Simulation and Computation, 21(4), p. 1001-1020.

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