# xcusum.crit: Compute decision intervals of CUSUM control charts In spc: Statistical Process Control -- Calculation of ARL and Other Control Chart Performance Measures

## Description

Computation of the decision intervals (alarm limits) for different types of CUSUM control charts monitoring normal mean.

## Usage

 `1` ```xcusum.crit(k, L0, mu0 = 0, hs = 0, sided = "one", r = 30) ```

## Arguments

 `k` reference value of the CUSUM control chart. `L0` in-control ARL. `mu0` in-control mean. `hs` so-called headstart (enables fast initial response). `sided` distinguishes between one-, two-sided and Crosier's modified two-sided CUSUM scheme by choosing `"one"`, `"two"`, and `"Crosier"`, respectively. `r` number of quadrature nodes, dimension of the resulting linear equation system is equal to `r+1` (one-, two-sided) or `2r+1` (Crosier).

## Details

`xcusum.crit` determines the decision interval (alarm limit) for given in-control ARL `L0` by applying secant rule and using `xcusum.arl()`.

## Value

Returns a single value which resembles the decision interval `h`.

## Author(s)

Sven Knoth

`xcusum.arl` for zero-state ARL computation.
 ```1 2 3 4 5``` ```k <- .5 incontrolARL <- c(500,5000,50000) sapply(incontrolARL,k=k,xcusum.crit,r=10) # accuracy with 10 nodes sapply(incontrolARL,k=k,xcusum.crit,r=20) # accuracy with 20 nodes sapply(incontrolARL,k=k,xcusum.crit) # accuracy with 30 nodes ```