Type: Package
Title: Compute Decision Interval and Average Run Length for CUSUM Charts
Version: 1.1.5
Date: 2020-02-22
Author: Douglas M. Hawkins, David H. Olwell, and Boxiang Wang
Maintainer: Boxiang Wang <boxiang-wang@uiowa.edu>
Description: Computation of decision intervals (H) and average run lengths (ARL) for CUSUM charts. Details of the method are seen in Hawkins and Olwell (2012): Cumulative sum charts and charting for quality improvement, Springer Science & Business Media.
License: GPL-2
Repository: CRAN
NeedsCompilation: yes
Packaged: 2020-02-23 17:34:15 UTC; boxiangw
Date/Publication: 2020-02-24 17:40:09 UTC

compute average run length (ARL) for CUSUM charts

Description

Compute average run lengths for CUSUM charts based on the Markov chain algorithm.

Usage

getARL(distr=NULL, K=NULL, H=NULL,
    Mean=NULL, std=NULL, prob=NULL, Var=NULL, mu=NULL, lambda=NULL, 
    samp.size=NULL, is.upward=NULL, winsrl=NULL, winsru=NULL)

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", and 6 refers to “inverse Gaussian mean".

K

A reference value, which is given by getH.

H

A given decision interval, which is given by getH.

Mean

Mean value, which has to be provided when distr = 1 (normal mean), 3 (Poisson), and 5 (negative binomial). The value must be positive when distr = 3 or distr = 5.

std

Standard deviation, which has to be provided when distr = 1 (normal mean) and 2 (normal variance). The value must be positive.

prob

Success probability, which has to be provided when distr = 4 (binomial); 0 < prob <= 1.

Var

Variance, which has to be provided when distr = 5 (negative binomial). The value has to be larger than Mean when distr = 5.

mu

A positive value representing the mean of inverse Gaussian distribution. The argument 'mu' has to be provided when distr = 6 (inverse Gaussian mean).

lambda

A positive value representing the shape parameter for inverse Gaussian distribution. The argument 'lambda' 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).

is.upward

Logical value, whether to depict a upward or downward CUSUM.

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.

Details

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

Normal mean (distr = 1): Mean, std, K, H.
Normal variance (distr = 2): samp.size, std, K, H.
Poisson (distr = 3): Mean, K, H.
Binomial (dist = 4): samp.size, prob, K, H.
Negative binomial (distr = 5): Mean, Var, K, H.
Inverse Gaussian mean (distr = 6): mu, lambda, K, H.

Value

A list including three variables:

ARL_Z

The computed zero-start average run length for CUSUM.

ARL_F

The computed fast-initial-response (FIR) average run length for CUSUM.

ARL_S

The computed steady-state average run length for 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.

See Also

getH

Examples

# normal mean
getARL(distr=1, K=11, H=5, Mean=10, std=2)

# normal variance
getARL(distr=2, K=3, H=1, std=2, samp.size=5, is.upward=TRUE)

# Poission
getARL(distr=3, K=3, H=1, std=2, Mean=5, is.upward=TRUE)

# Binomial
getARL(distr=4, K=0.8, H=1, prob=0.2, samp.size=100, is.upward=TRUE)

# Negative binomial
getARL(distr=5, K=3, H=6, Mean=2, Var=5, is.upward=TRUE)

# Inverse Gaussian mean
getARL(distr=6, K=2, H=4, mu=3, lambda=0.5, is.upward=TRUE)

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.

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")