| Title: | Compute Decision Interval and Average Run Length for CUSUM Charts |
|---|---|
| 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. |
| Authors: | Douglas M. Hawkins, David H. Olwell, and Boxiang Wang |
| Maintainer: | Boxiang Wang <[email protected]> |
| License: | GPL-2 |
| Version: | 1.1.5 |
| Built: | 2025-01-13 04:17:37 UTC |
| Source: | https://github.com/boxiang-wang/cusumdesign |
Compute average run lengths for CUSUM charts based on the Markov chain algorithm.
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)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)
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 |
H |
A given decision interval, which is given by |
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. |
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.
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. |
Douglas M. Hawkins, David H. Olwell, and Boxiang Wang
Maintainer: Boxiang Wang [email protected]
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 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)# 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 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"))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 [email protected]
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")# 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")