# arl: ARL for Lucas's Cusum Chart for Attribute Data In IAcsSPCR: Data and Functions for "An Intro. to Accept. Samp. & SPC/R"

## Description

Calculates ARL for Lucas's Cusum Chart for Attribute Data

## Usage

 `1` ```arl(h=2,k=2,lambda=1,shift=.5) ```

## Arguments

 `h` input - this is the decision limit. It should be an even number, so that h/2 for the FIR feature will also be an integer. `k` input - this is the reference value. It should be calculated as (mu_d-mu_a)/ln(mu_d-mu_a), where mu_a is the in-control Poisson mean and mu_d mean to detect. k should be rounded to an integer. `lambda` input - this is the in-control Poisson mean. `shift` input - this is the number of standard deviation shift from the in-control mean to the mean to detect , i.e., lambda+shift*sqrt(lambda)=mu_d.

## Value

returned list containing the ARL and the ARL with FIR.

John Lawson

## References

Lucas, J.M.(1985) "Counted data cusums", Technometrics, Vol. 27, No. 2, pp129-143.

## Examples

 ```1 2 3 4 5``` ```library(IAcsSPCR) arl(h=6,k=2,lambda=1.88,shift=0) arl(h=6,k=2,lambda=1.88,shift=.9627) { } ```

### Example output

```Registered S3 method overwritten by 'DoE.base':
method           from
factorize.factor conf.design
[]
 "ARL="

[]
 37.2

[]
 " ARL(FIR)="

[]
 29.19

[]
 " Valid if h is a even integer "

[]
 "ARL="

[]
 5.49

[]
 " ARL(FIR)="

[]
 3.33

[]
 " Valid if h is a even integer "

NULL
```

IAcsSPCR documentation built on Nov. 23, 2020, 5:07 p.m.