getH {CUSUMdesign} | R Documentation |

Compute decision intervals for CUSUM charts.

```
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"))
```

`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". |

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.`

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. |

Douglas M. Hawkins, David H. Olwell, and Boxiang Wang

Maintainer: Boxiang Wang boxiang-wang@uiowa.edu

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

```
# 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]