getH {CUSUMdesign}

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 [e-mail]

References

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

See Also

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")