getH {CUSUMdesign} R Documentation

## compute decision interval (H) for CUSUM charts

### Description

Compute decision intervals for CUSUM charts.

### Usage

```getH(distr=NULL, ARL=NULL, ICmean=NULL, ICsd=NULL,
OOCmean=NULL, OOCsd=NULL, ICprob=NULL, OOCprob=NULL,
ICvar=NULL, IClambda=NULL, samp.size=NULL,
ref=NULL, winsrl=NULL, winsru=NULL,
type=c("fast initial response", "zero start", "steady state"))
```

### Arguments

 `distr` Integer valued from 1 to 6: 1 refers to “normal mean", 2 refers to “normal variance", 3 refers to “Poisson", 4 refers to “binomial", 5 refers to “negative binomial", 6 refers to “inverse Gaussian mean". `ARL` An integer for in control average run length. `ICmean` In-control mean, which has to be provided when distr = 1 (normal mean), 3 (Poisson), 5 (negative binomial), and 6 (inverse Gaussian mean). The value has to be positive when distr = 3, distr = 5, or distr = 6. `ICsd` In-control standard deviation, which has to be provided when distr = 1 (normal mean) and 2 (normal variance). The value has to be positive. `OOCmean` Out-of-control mean, which has to be provided when distr = 1 (normal mean), 3 (Poisson), 5 (negative binomial), and 6 (Inverse Gaussian mean). When distr = 3, 5, or 6, the value has to be positive. `OOCsd` Out-of-control standard deviation, which has to be provided when distr = 2 (normal variance). The value has to be positive. `ICprob` In-control success probability, which has to be provided when distr = 4 (binomial); 0 < prob <= 1. `OOCprob` Out-of-control success probability, which has to be provided when distr = 4 (binomial); 0 < prob <= 1. `ICvar` In-control variance, which has to be provided when distr = 5 (negative binomial). The value has to be larger than the in-control mean 'ICmean'. `IClambda` In-control shape parameter for inverse Gaussian distribution. The argument 'IClambda' has to be provided when distr = 6 (inverse Gaussian mean). `samp.size` Sample size, an integer which has to be provided when distr = 2 (normal variance) or distr = 4 (binomial). `ref` Optional reference value. `winsrl` Lower Winsorizing constant. Use NULL or -999 if Winsorization is not needed. `winsru` Upper Winsorizing constant. Use NULL or 999 if Winsorization is not needed. `type` A string for CUSUM type: "F" for fast-initial-response CUSUM, "Z" for zero-start CUSUM, and "S" for steady-state CUSUM. Default is "F".

### Details

Computes the decision interval H when the reference value and the average run length are given. For each case, the necessary parameters are listed as follows.

Normal mean (distr = 1): `ICmean`, `ICsd`, `OOCmean`.
Normal variance (distr = 2): `samp.size`, `ICsd`, `OOCsd`
Poisson (distr = 3): `ICmean`, `OOCmean`.
Binomial (dist = 4): `samp.size`, `ICprob`, `OOCprob`.
Negative binomial (distr = 5): `ICmean`, `Icvar`, `OOCmean`.
Inverse Gaussian mean (distr = 6): `ICmean`, `IClambda`, `OOCmean.`

### Value

A list including three variables:

 `DI` Decision interval. `IC_ARL` In-control average run length. `OOCARL_Z` Out-of-control average run length for the zero-start CUSUM. `OOCARL_F` Out-of-control average run length for the fast-initial-response (FIR) CUSUM. `OOCARL_S` Out-of-control average run length for the steady-state CUSUM.

### Author(s)

Douglas M. Hawkins, David H. Olwell, and Boxiang Wang
Maintainer: Boxiang Wang boxiang-wang@uiowa.edu

### References

Hawkins, D. M. and Olwell, D. H. (1998) “Cumulative Sum Charts and Charting for Quality Improvement (Information Science and Statistics)", Springer, New York.

`getARL`

### Examples

```# normal mean
getH(distr=1, ICmean=10, ICsd=2, OOCmean=15, ARL=1000, type="F")

# normal variance
getH(distr=2, ICsd=2, OOCsd=4, samp.size=5, ARL=1000, type="F")

# Poission
getH(distr=3, ICmean=2, OOCmean=3, ARL=100, type="F")

# Binomial
getH(distr=4, ICprob=0.2, OOCprob=0.6, samp.size=100, ARL=1000, type="F")

# Negative binomial
getH(distr=5, ICmean=1, ICvar=3, OOCmean=2, ARL=100, type="F")

# Inverse Gaussian mean
getH(distr=6, ICmean=1, IClambda=0.5, OOCmean=2, ARL=1000, type="F")
```

[Package CUSUMdesign version 1.1.5 Index]