Description Usage Arguments Details Value Author(s) References See Also Examples
Compute decision intervals for CUSUM charts.
1 2 3 4 5 |
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.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 | # 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")
|
The reference value is 12.500
DI 4.222 IC ARL 1000.0 OOC ARL Zero start 2.4
FIR 1.6 SS 1.0
$DI
[1] 4.222265
$ref
[1] 12.5
$IC_ARL
[1] 999.9994
$OOCARL_Z
[1] 2.392417
$OOCARL_F
[1] 1.622589
$OOCARL_S
[1] 0.9661677
The reference value is 7.394
DI 12.621 IC ARL 1000.0 OOC ARL Zero start 2.6
FIR 2.0 SS 1.3
$DI
[1] 12.62062
$ref
[1] 7.39357
$IC_ARL
[1] 1000
$OOCARL_Z
[1] 2.597972
$OOCARL_F
[1] 2.006911
$OOCARL_S
[1] 1.325745
The reference value is 2.466
k 2.4444 h 6.3333 ARL 99.64
h 6.4444 ARL 105.02
DI 6.444 IC ARL 105.0 OOC ARL Zero start 11.0
FIR 7.4 SS 7.4
$DI
[1] 6.444444
$ref
[1] 2.444444
$IC_ARL
[1] 105.0164
$OOCARL_Z
[1] 10.96038
$OOCARL_F
[1] 7.375915
$OOCARL_S
[1] 7.441145
The reference value is 38.685
k 38.6667 h 0.0000 ARL 1.00
h 0.3333 ARL 103265.32
DI 0.333 IC ARL 103265.3 OOC ARL Zero start 1.0
FIR 1.0 SS 0.0
$DI
[1] 0.3333333
$ref
[1] 38.66667
$IC_ARL
[1] 103265.3
$OOCARL_Z
[1] 1.000007
$OOCARL_F
[1] 1.000007
$OOCARL_S
[1] 7.363954e-06
The reference value is 1.401
k 1.4009 h 10.0000 ARL 99.83
h 10.2000 ARL 103.87
DI 10.200 IC ARL 103.9 OOC ARL Zero start 15.7
FIR 12.2 SS 12.8
$DI
[1] 10.2
$ref
[1] 1.400892
$IC_ARL
[1] 103.8682
$OOCARL_Z
[1] 15.68369
$OOCARL_F
[1] 12.17098
$OOCARL_S
[1] 12.77594
The reference value is 1.333
DI 18.183 IC ARL 999.5 OOC ARL Zero start 30.8
FIR 22.8 SS 25.1
$DI
[1] 18.18331
$ref
[1] 1.333333
$IC_ARL
[1] 999.4661
$OOCARL_Z
[1] 30.78667
$OOCARL_F
[1] 22.75136
$OOCARL_S
[1] 25.07536
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