oc.curves: Operating Characteristic Function
In qcc: Quality Control Charts
Description
Usage
Arguments
Details
Value
Author(s)
References
See Also
Examples
Description
Draws the operating characteristic curves for a 'qcc' object.
Usage
1
2
3
4
5
6
7
8
9
10
11
12
13
14
oc.curves(object, ...)
oc.curves.xbar(object, n, c = seq(0, 5, length=101),
nsigmas = object$nsigmas, identify=FALSE, restore.par=TRUE)
oc.curves.R(object, n, c = seq(1, 6, length=101),
nsigmas = object$nsigmas, identify = FALSE, restore.par=TRUE)
oc.curves.S(object, n, c = seq(1, 6, length=101),
nsigmas = object$nsigmas, identify = FALSE, restore.par=TRUE)
oc.curves.p(object, nsigmas = object$nsigmas, identify = FALSE, restore.par=TRUE)
oc.curves.c(object, nsigmas = object$nsigmas, identify = FALSE, restore.par=TRUE)
Arguments
object
an object of class 'qcc'.
identify
logical specifying whether to interactively identify points on the plot (see help for identify).
n
a vector of values specifying the sample sizes for which to draw the OC curves.
c
a vector of values specifying the multipliers for sigma in case of continuous variable.
nsigmas
a numeric value specifying the number of sigmas to use for
computing control limits; if nsigmas is NULL,
object$conf is used to set up probability limits; nsigmas
is ignored for types "p" and "c".
restore.par
a logical value indicating whether the previous par settings must be restored. If you need to add points, lines, etc. to a chart set this to FALSE.
...
additional arguments to be passed to the generic function.
Details
An operating characteristic curve graphically provides information about the probability of not detecting a shift in the process. oc.curves is a generic function which calls the proper function depending on the type of 'qcc' object. Further arguments provided through ... are passed to the specific function depending on the type of chart.
The probabilities are based on the conventional assumptions about
process distributions: the normal distribution for "xbar" , "R", and "S",
the binomial distribution for "p" and "np", and the Poisson distribution
for "c" and "u". They are all sensitive to departures from those assumptions,
but to varying degrees. The performance of the "S" chart, and especially
the "R" chart,
are likely to be seriously affected by longer tails.
Value
The function invisibly returns a matrix or a vector of beta values, the probability of type II error.
Author(s)
Luca Scrucca
References
Mason, R.L. and Young, J.C. (2002) Multivariate Statistical Process Control with Industrial Applications, SIAM.
Montgomery, D.C. (2005) Introduction to Statistical Quality Control, 5th ed. New York: John Wiley & Sons.
Ryan, T. P. (2000), Statistical Methods for Quality Improvement, 2nd ed. New York: John Wiley & Sons, Inc.
Scrucca, L. (2004). qcc: an R package for quality control charting and statistical process control. R News 4/1, 11-17.
Wetherill, G.B. and Brown, D.W. (1991) Statistical Process Control. New York: Chapman & Hall.
See Also
Examples
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
data(pistonrings)
attach(pistonrings)
diameter <- qcc.groups(diameter, sample)
beta <- oc.curves.xbar(qcc(diameter, type="xbar", nsigmas=3, plot=FALSE))
print(round(beta, digits=4))
# or to identify points on the plot use
## Not run: oc.curves.xbar(qcc(diameter, type="xbar", nsigmas=3, plot=FALSE), identify=TRUE)
detach(pistonrings)
data(orangejuice)
attach(orangejuice)
beta <- oc.curves(qcc(D[trial], sizes=size[trial], type="p", plot=FALSE))
print(round(beta, digits=4))
# or to identify points on the plot use
## Not run: oc.curves(qcc(D[trial], sizes=size[trial], type="p", plot=FALSE), identify=TRUE)
detach(orangejuice)
data(circuit)
attach(circuit)
q <- qcc(x[trial], sizes=size[trial], type="c", plot=FALSE)
beta <- oc.curves(q)
print(round(beta, digits=4))
# or to identify points on the plot use
## Not run: oc.curves(qcc(x[trial], sizes=size[trial], type="c", plot=FALSE), identify=TRUE)
detach(circuit)
Example output
Package 'qcc' version 2.7
Type 'citation("qcc")' for citing this R package in publications.
sample size
shift (std.dev) n=5 n=1 n=10 n=15 n=20
0 0.9973 0.9973 0.9973 0.9973 0.9973
0.05 0.9971 0.9973 0.9970 0.9968 0.9966
0.1 0.9966 0.9972 0.9959 0.9952 0.9944
0.15 0.9957 0.9970 0.9940 0.9920 0.9900
0.2 0.9944 0.9968 0.9909 0.9869 0.9823
0.25 0.9925 0.9964 0.9864 0.9789 0.9701
0.3 0.9900 0.9960 0.9798 0.9670 0.9514
0.35 0.9866 0.9956 0.9708 0.9500 0.9243
0.4 0.9823 0.9950 0.9586 0.9266 0.8871
0.45 0.9769 0.9943 0.9426 0.8957 0.8383
0.5 0.9701 0.9936 0.9220 0.8562 0.7775
0.55 0.9616 0.9927 0.8963 0.8078 0.7055
0.6 0.9514 0.9916 0.8649 0.7505 0.6243
0.65 0.9390 0.9905 0.8275 0.6853 0.5371
0.7 0.9243 0.9892 0.7842 0.6137 0.4481
0.75 0.9071 0.9877 0.7351 0.5379 0.3616
0.8 0.8871 0.9860 0.6809 0.4608 0.2817
0.85 0.8642 0.9842 0.6225 0.3851 0.2115
0.9 0.8383 0.9821 0.5612 0.3136 0.1527
0.95 0.8094 0.9798 0.4983 0.2485 0.1059
1 0.7775 0.9772 0.4355 0.1913 0.0705
1.05 0.7428 0.9744 0.3743 0.1431 0.0450
1.1 0.7055 0.9713 0.3161 0.1038 0.0275
1.15 0.6659 0.9678 0.2622 0.0730 0.0161
1.2 0.6243 0.9641 0.2134 0.0497 0.0090
1.25 0.5812 0.9599 0.1703 0.0328 0.0048
1.3 0.5371 0.9554 0.1333 0.0209 0.0024
1.35 0.4925 0.9505 0.1022 0.0129 0.0012
1.4 0.4481 0.9452 0.0768 0.0077 0.0006
1.45 0.4043 0.9394 0.0564 0.0045 0.0002
1.5 0.3616 0.9332 0.0406 0.0025 0.0001
1.55 0.3206 0.9265 0.0286 0.0013 0.0000
1.6 0.2817 0.9192 0.0197 0.0007 0.0000
1.65 0.2453 0.9115 0.0133 0.0003 0.0000
1.7 0.2115 0.9032 0.0088 0.0002 0.0000
1.75 0.1806 0.8943 0.0056 0.0001 0.0000
1.8 0.1527 0.8849 0.0036 0.0000 0.0000
1.85 0.1278 0.8749 0.0022 0.0000 0.0000
1.9 0.1059 0.8643 0.0013 0.0000 0.0000
1.95 0.0869 0.8531 0.0008 0.0000 0.0000
2 0.0705 0.8413 0.0004 0.0000 0.0000
2.05 0.0566 0.8289 0.0002 0.0000 0.0000
2.1 0.0450 0.8159 0.0001 0.0000 0.0000
2.15 0.0353 0.8023 0.0001 0.0000 0.0000
2.2 0.0275 0.7881 0.0000 0.0000 0.0000
2.25 0.0211 0.7734 0.0000 0.0000 0.0000
2.3 0.0161 0.7580 0.0000 0.0000 0.0000
2.35 0.0121 0.7422 0.0000 0.0000 0.0000
2.4 0.0090 0.7257 0.0000 0.0000 0.0000
2.45 0.0066 0.7088 0.0000 0.0000 0.0000
2.5 0.0048 0.6915 0.0000 0.0000 0.0000
2.55 0.0034 0.6736 0.0000 0.0000 0.0000
2.6 0.0024 0.6554 0.0000 0.0000 0.0000
2.65 0.0017 0.6368 0.0000 0.0000 0.0000
2.7 0.0012 0.6179 0.0000 0.0000 0.0000
2.75 0.0008 0.5987 0.0000 0.0000 0.0000
2.8 0.0006 0.5793 0.0000 0.0000 0.0000
2.85 0.0004 0.5596 0.0000 0.0000 0.0000
2.9 0.0002 0.5398 0.0000 0.0000 0.0000
2.95 0.0002 0.5199 0.0000 0.0000 0.0000
3 0.0001 0.5000 0.0000 0.0000 0.0000
3.05 0.0001 0.4801 0.0000 0.0000 0.0000
3.1 0.0000 0.4602 0.0000 0.0000 0.0000
3.15 0.0000 0.4404 0.0000 0.0000 0.0000
3.2 0.0000 0.4207 0.0000 0.0000 0.0000
3.25 0.0000 0.4013 0.0000 0.0000 0.0000
3.3 0.0000 0.3821 0.0000 0.0000 0.0000
3.35 0.0000 0.3632 0.0000 0.0000 0.0000
3.4 0.0000 0.3446 0.0000 0.0000 0.0000
3.45 0.0000 0.3264 0.0000 0.0000 0.0000
3.5 0.0000 0.3085 0.0000 0.0000 0.0000
3.55 0.0000 0.2912 0.0000 0.0000 0.0000
3.6 0.0000 0.2743 0.0000 0.0000 0.0000
3.65 0.0000 0.2578 0.0000 0.0000 0.0000
3.7 0.0000 0.2420 0.0000 0.0000 0.0000
3.75 0.0000 0.2266 0.0000 0.0000 0.0000
3.8 0.0000 0.2119 0.0000 0.0000 0.0000
3.85 0.0000 0.1977 0.0000 0.0000 0.0000
3.9 0.0000 0.1841 0.0000 0.0000 0.0000
3.95 0.0000 0.1711 0.0000 0.0000 0.0000
4 0.0000 0.1587 0.0000 0.0000 0.0000
4.05 0.0000 0.1469 0.0000 0.0000 0.0000
4.1 0.0000 0.1357 0.0000 0.0000 0.0000
4.15 0.0000 0.1251 0.0000 0.0000 0.0000
4.2 0.0000 0.1151 0.0000 0.0000 0.0000
4.25 0.0000 0.1056 0.0000 0.0000 0.0000
4.3 0.0000 0.0968 0.0000 0.0000 0.0000
4.35 0.0000 0.0885 0.0000 0.0000 0.0000
4.4 0.0000 0.0808 0.0000 0.0000 0.0000
4.45 0.0000 0.0735 0.0000 0.0000 0.0000
4.5 0.0000 0.0668 0.0000 0.0000 0.0000
4.55 0.0000 0.0606 0.0000 0.0000 0.0000
4.6 0.0000 0.0548 0.0000 0.0000 0.0000
4.65 0.0000 0.0495 0.0000 0.0000 0.0000
4.7 0.0000 0.0446 0.0000 0.0000 0.0000
4.75 0.0000 0.0401 0.0000 0.0000 0.0000
4.8 0.0000 0.0359 0.0000 0.0000 0.0000
4.85 0.0000 0.0322 0.0000 0.0000 0.0000
4.9 0.0000 0.0287 0.0000 0.0000 0.0000
4.95 0.0000 0.0256 0.0000 0.0000 0.0000
5 0.0000 0.0228 0.0000 0.0000 0.0000
Warning message:
In oc.curves.p(object, ...) :
Some computed values for the type II error have been rounded due to the discreteness of the binomial distribution. Thus, some ARL values might be meaningless.
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
0.0000 0.0894 0.2642 0.4447 0.5995 0.7206 0.8100 0.8735 0.9173 0.9468 0.9662
0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2 0.21
0.9788 0.9869 0.9920 0.9951 0.9971 0.9983 0.9990 0.9993 0.9995 0.9995 0.9993
0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.3 0.31 0.32
0.9987 0.9978 0.9962 0.9937 0.9900 0.9845 0.9768 0.9662 0.9522 0.9343 0.9118
0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.4 0.41 0.42 0.43
0.8844 0.8518 0.8139 0.7711 0.7236 0.6722 0.6176 0.5610 0.5035 0.4461 0.3901
0.44 0.45 0.46 0.47 0.48 0.49 0.5 0.51 0.52 0.53 0.54
0.3365 0.2862 0.2398 0.1980 0.1609 0.1287 0.1013 0.0784 0.0596 0.0446 0.0327
0.55 0.56 0.57 0.58 0.59 0.6 0.61 0.62 0.63 0.64 0.65
0.0235 0.0166 0.0115 0.0078 0.0052 0.0034 0.0021 0.0013 0.0008 0.0005 0.0003
0.66 0.67 0.68 0.69 0.7 0.71 0.72 0.73 0.74 0.75 0.76
0.0002 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
0.77 0.78 0.79 0.8 0.81 0.82 0.83 0.84 0.85 0.86 0.87
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
0.88 0.89 0.9 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
0.99 1
0.0000 0.0000
Warning message:
In oc.curves.c(object, ...) :
Some computed values for the type II error have been rounded due to the discreteness of the Poisson distribution. Thus, some ARL values might be meaningless.
0 1 2 3 4 5 6 7 8 9 10
0.0000 0.0006 0.0166 0.0839 0.2149 0.3840 0.5543 0.6993 0.8088 0.8843 0.9329
11 12 13 14 15 16 17 18 19 20 21
0.9625 0.9797 0.9893 0.9945 0.9972 0.9986 0.9991 0.9992 0.9986 0.9972 0.9945
22 23 24 25 26 27 28 29 30 31 32
0.9895 0.9813 0.9686 0.9502 0.9249 0.8918 0.8505 0.8011 0.7444 0.6818 0.6150
33 34 35 36 37 38 39 40 41 42 43
0.5461 0.4772 0.4102 0.3470 0.2888 0.2365 0.1907 0.1514 0.1184 0.0912 0.0693
44 45 46 47 48 49 50 51 52 53 54
0.0519 0.0383 0.0280 0.0201 0.0143 0.0101 0.0070 0.0048 0.0033 0.0022 0.0015
55 56 57 58 59 60 61 62 63 64 65
0.0010 0.0006 0.0004 0.0003 0.0002 0.0001 0.0001 0.0000 0.0000 0.0000 0.0000
qcc documentation built on May 2, 2019, 9:15 a.m.
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Description Usage Arguments Details Value Author(s) References See Also Examples
Description
Draws the operating characteristic curves for a 'qcc' object.
Usage
1 2 3 4 5 6 7 8 9 10 11 12 13 14 | oc.curves(object, ...)
oc.curves.xbar(object, n, c = seq(0, 5, length=101),
nsigmas = object$nsigmas, identify=FALSE, restore.par=TRUE)
oc.curves.R(object, n, c = seq(1, 6, length=101),
nsigmas = object$nsigmas, identify = FALSE, restore.par=TRUE)
oc.curves.S(object, n, c = seq(1, 6, length=101),
nsigmas = object$nsigmas, identify = FALSE, restore.par=TRUE)
oc.curves.p(object, nsigmas = object$nsigmas, identify = FALSE, restore.par=TRUE)
oc.curves.c(object, nsigmas = object$nsigmas, identify = FALSE, restore.par=TRUE)
|
Arguments
object |
an object of class 'qcc'. |
identify |
logical specifying whether to interactively identify points on the plot (see help for |
n |
a vector of values specifying the sample sizes for which to draw the OC curves. |
c |
a vector of values specifying the multipliers for sigma in case of continuous variable. |
nsigmas |
a numeric value specifying the number of sigmas to use for
computing control limits; if |
restore.par |
a logical value indicating whether the previous |
... |
additional arguments to be passed to the generic function. |
Details
An operating characteristic curve graphically provides information about the probability of not detecting a shift in the process. oc.curves is a generic function which calls the proper function depending on the type of 'qcc' object. Further arguments provided through ... are passed to the specific function depending on the type of chart.
The probabilities are based on the conventional assumptions about process distributions: the normal distribution for "xbar" , "R", and "S", the binomial distribution for "p" and "np", and the Poisson distribution for "c" and "u". They are all sensitive to departures from those assumptions, but to varying degrees. The performance of the "S" chart, and especially the "R" chart, are likely to be seriously affected by longer tails.
Value
The function invisibly returns a matrix or a vector of beta values, the probability of type II error.
Author(s)
Luca Scrucca
References
Mason, R.L. and Young, J.C. (2002) Multivariate Statistical Process Control with Industrial Applications, SIAM.
Montgomery, D.C. (2005) Introduction to Statistical Quality Control, 5th ed. New York: John Wiley & Sons.
Ryan, T. P. (2000), Statistical Methods for Quality Improvement, 2nd ed. New York: John Wiley & Sons, Inc.
Scrucca, L. (2004). qcc: an R package for quality control charting and statistical process control. R News 4/1, 11-17.
Wetherill, G.B. and Brown, D.W. (1991) Statistical Process Control. New York: Chapman & Hall.
See Also
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 | data(pistonrings)
attach(pistonrings)
diameter <- qcc.groups(diameter, sample)
beta <- oc.curves.xbar(qcc(diameter, type="xbar", nsigmas=3, plot=FALSE))
print(round(beta, digits=4))
# or to identify points on the plot use
## Not run: oc.curves.xbar(qcc(diameter, type="xbar", nsigmas=3, plot=FALSE), identify=TRUE)
detach(pistonrings)
data(orangejuice)
attach(orangejuice)
beta <- oc.curves(qcc(D[trial], sizes=size[trial], type="p", plot=FALSE))
print(round(beta, digits=4))
# or to identify points on the plot use
## Not run: oc.curves(qcc(D[trial], sizes=size[trial], type="p", plot=FALSE), identify=TRUE)
detach(orangejuice)
data(circuit)
attach(circuit)
q <- qcc(x[trial], sizes=size[trial], type="c", plot=FALSE)
beta <- oc.curves(q)
print(round(beta, digits=4))
# or to identify points on the plot use
## Not run: oc.curves(qcc(x[trial], sizes=size[trial], type="c", plot=FALSE), identify=TRUE)
detach(circuit)
|
Example output
Package 'qcc' version 2.7
Type 'citation("qcc")' for citing this R package in publications.
sample size
shift (std.dev) n=5 n=1 n=10 n=15 n=20
0 0.9973 0.9973 0.9973 0.9973 0.9973
0.05 0.9971 0.9973 0.9970 0.9968 0.9966
0.1 0.9966 0.9972 0.9959 0.9952 0.9944
0.15 0.9957 0.9970 0.9940 0.9920 0.9900
0.2 0.9944 0.9968 0.9909 0.9869 0.9823
0.25 0.9925 0.9964 0.9864 0.9789 0.9701
0.3 0.9900 0.9960 0.9798 0.9670 0.9514
0.35 0.9866 0.9956 0.9708 0.9500 0.9243
0.4 0.9823 0.9950 0.9586 0.9266 0.8871
0.45 0.9769 0.9943 0.9426 0.8957 0.8383
0.5 0.9701 0.9936 0.9220 0.8562 0.7775
0.55 0.9616 0.9927 0.8963 0.8078 0.7055
0.6 0.9514 0.9916 0.8649 0.7505 0.6243
0.65 0.9390 0.9905 0.8275 0.6853 0.5371
0.7 0.9243 0.9892 0.7842 0.6137 0.4481
0.75 0.9071 0.9877 0.7351 0.5379 0.3616
0.8 0.8871 0.9860 0.6809 0.4608 0.2817
0.85 0.8642 0.9842 0.6225 0.3851 0.2115
0.9 0.8383 0.9821 0.5612 0.3136 0.1527
0.95 0.8094 0.9798 0.4983 0.2485 0.1059
1 0.7775 0.9772 0.4355 0.1913 0.0705
1.05 0.7428 0.9744 0.3743 0.1431 0.0450
1.1 0.7055 0.9713 0.3161 0.1038 0.0275
1.15 0.6659 0.9678 0.2622 0.0730 0.0161
1.2 0.6243 0.9641 0.2134 0.0497 0.0090
1.25 0.5812 0.9599 0.1703 0.0328 0.0048
1.3 0.5371 0.9554 0.1333 0.0209 0.0024
1.35 0.4925 0.9505 0.1022 0.0129 0.0012
1.4 0.4481 0.9452 0.0768 0.0077 0.0006
1.45 0.4043 0.9394 0.0564 0.0045 0.0002
1.5 0.3616 0.9332 0.0406 0.0025 0.0001
1.55 0.3206 0.9265 0.0286 0.0013 0.0000
1.6 0.2817 0.9192 0.0197 0.0007 0.0000
1.65 0.2453 0.9115 0.0133 0.0003 0.0000
1.7 0.2115 0.9032 0.0088 0.0002 0.0000
1.75 0.1806 0.8943 0.0056 0.0001 0.0000
1.8 0.1527 0.8849 0.0036 0.0000 0.0000
1.85 0.1278 0.8749 0.0022 0.0000 0.0000
1.9 0.1059 0.8643 0.0013 0.0000 0.0000
1.95 0.0869 0.8531 0.0008 0.0000 0.0000
2 0.0705 0.8413 0.0004 0.0000 0.0000
2.05 0.0566 0.8289 0.0002 0.0000 0.0000
2.1 0.0450 0.8159 0.0001 0.0000 0.0000
2.15 0.0353 0.8023 0.0001 0.0000 0.0000
2.2 0.0275 0.7881 0.0000 0.0000 0.0000
2.25 0.0211 0.7734 0.0000 0.0000 0.0000
2.3 0.0161 0.7580 0.0000 0.0000 0.0000
2.35 0.0121 0.7422 0.0000 0.0000 0.0000
2.4 0.0090 0.7257 0.0000 0.0000 0.0000
2.45 0.0066 0.7088 0.0000 0.0000 0.0000
2.5 0.0048 0.6915 0.0000 0.0000 0.0000
2.55 0.0034 0.6736 0.0000 0.0000 0.0000
2.6 0.0024 0.6554 0.0000 0.0000 0.0000
2.65 0.0017 0.6368 0.0000 0.0000 0.0000
2.7 0.0012 0.6179 0.0000 0.0000 0.0000
2.75 0.0008 0.5987 0.0000 0.0000 0.0000
2.8 0.0006 0.5793 0.0000 0.0000 0.0000
2.85 0.0004 0.5596 0.0000 0.0000 0.0000
2.9 0.0002 0.5398 0.0000 0.0000 0.0000
2.95 0.0002 0.5199 0.0000 0.0000 0.0000
3 0.0001 0.5000 0.0000 0.0000 0.0000
3.05 0.0001 0.4801 0.0000 0.0000 0.0000
3.1 0.0000 0.4602 0.0000 0.0000 0.0000
3.15 0.0000 0.4404 0.0000 0.0000 0.0000
3.2 0.0000 0.4207 0.0000 0.0000 0.0000
3.25 0.0000 0.4013 0.0000 0.0000 0.0000
3.3 0.0000 0.3821 0.0000 0.0000 0.0000
3.35 0.0000 0.3632 0.0000 0.0000 0.0000
3.4 0.0000 0.3446 0.0000 0.0000 0.0000
3.45 0.0000 0.3264 0.0000 0.0000 0.0000
3.5 0.0000 0.3085 0.0000 0.0000 0.0000
3.55 0.0000 0.2912 0.0000 0.0000 0.0000
3.6 0.0000 0.2743 0.0000 0.0000 0.0000
3.65 0.0000 0.2578 0.0000 0.0000 0.0000
3.7 0.0000 0.2420 0.0000 0.0000 0.0000
3.75 0.0000 0.2266 0.0000 0.0000 0.0000
3.8 0.0000 0.2119 0.0000 0.0000 0.0000
3.85 0.0000 0.1977 0.0000 0.0000 0.0000
3.9 0.0000 0.1841 0.0000 0.0000 0.0000
3.95 0.0000 0.1711 0.0000 0.0000 0.0000
4 0.0000 0.1587 0.0000 0.0000 0.0000
4.05 0.0000 0.1469 0.0000 0.0000 0.0000
4.1 0.0000 0.1357 0.0000 0.0000 0.0000
4.15 0.0000 0.1251 0.0000 0.0000 0.0000
4.2 0.0000 0.1151 0.0000 0.0000 0.0000
4.25 0.0000 0.1056 0.0000 0.0000 0.0000
4.3 0.0000 0.0968 0.0000 0.0000 0.0000
4.35 0.0000 0.0885 0.0000 0.0000 0.0000
4.4 0.0000 0.0808 0.0000 0.0000 0.0000
4.45 0.0000 0.0735 0.0000 0.0000 0.0000
4.5 0.0000 0.0668 0.0000 0.0000 0.0000
4.55 0.0000 0.0606 0.0000 0.0000 0.0000
4.6 0.0000 0.0548 0.0000 0.0000 0.0000
4.65 0.0000 0.0495 0.0000 0.0000 0.0000
4.7 0.0000 0.0446 0.0000 0.0000 0.0000
4.75 0.0000 0.0401 0.0000 0.0000 0.0000
4.8 0.0000 0.0359 0.0000 0.0000 0.0000
4.85 0.0000 0.0322 0.0000 0.0000 0.0000
4.9 0.0000 0.0287 0.0000 0.0000 0.0000
4.95 0.0000 0.0256 0.0000 0.0000 0.0000
5 0.0000 0.0228 0.0000 0.0000 0.0000
Warning message:
In oc.curves.p(object, ...) :
Some computed values for the type II error have been rounded due to the discreteness of the binomial distribution. Thus, some ARL values might be meaningless.
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
0.0000 0.0894 0.2642 0.4447 0.5995 0.7206 0.8100 0.8735 0.9173 0.9468 0.9662
0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2 0.21
0.9788 0.9869 0.9920 0.9951 0.9971 0.9983 0.9990 0.9993 0.9995 0.9995 0.9993
0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.3 0.31 0.32
0.9987 0.9978 0.9962 0.9937 0.9900 0.9845 0.9768 0.9662 0.9522 0.9343 0.9118
0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.4 0.41 0.42 0.43
0.8844 0.8518 0.8139 0.7711 0.7236 0.6722 0.6176 0.5610 0.5035 0.4461 0.3901
0.44 0.45 0.46 0.47 0.48 0.49 0.5 0.51 0.52 0.53 0.54
0.3365 0.2862 0.2398 0.1980 0.1609 0.1287 0.1013 0.0784 0.0596 0.0446 0.0327
0.55 0.56 0.57 0.58 0.59 0.6 0.61 0.62 0.63 0.64 0.65
0.0235 0.0166 0.0115 0.0078 0.0052 0.0034 0.0021 0.0013 0.0008 0.0005 0.0003
0.66 0.67 0.68 0.69 0.7 0.71 0.72 0.73 0.74 0.75 0.76
0.0002 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
0.77 0.78 0.79 0.8 0.81 0.82 0.83 0.84 0.85 0.86 0.87
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
0.88 0.89 0.9 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
0.99 1
0.0000 0.0000
Warning message:
In oc.curves.c(object, ...) :
Some computed values for the type II error have been rounded due to the discreteness of the Poisson distribution. Thus, some ARL values might be meaningless.
0 1 2 3 4 5 6 7 8 9 10
0.0000 0.0006 0.0166 0.0839 0.2149 0.3840 0.5543 0.6993 0.8088 0.8843 0.9329
11 12 13 14 15 16 17 18 19 20 21
0.9625 0.9797 0.9893 0.9945 0.9972 0.9986 0.9991 0.9992 0.9986 0.9972 0.9945
22 23 24 25 26 27 28 29 30 31 32
0.9895 0.9813 0.9686 0.9502 0.9249 0.8918 0.8505 0.8011 0.7444 0.6818 0.6150
33 34 35 36 37 38 39 40 41 42 43
0.5461 0.4772 0.4102 0.3470 0.2888 0.2365 0.1907 0.1514 0.1184 0.0912 0.0693
44 45 46 47 48 49 50 51 52 53 54
0.0519 0.0383 0.0280 0.0201 0.0143 0.0101 0.0070 0.0048 0.0033 0.0022 0.0015
55 56 57 58 59 60 61 62 63 64 65
0.0010 0.0006 0.0004 0.0003 0.0002 0.0001 0.0001 0.0000 0.0000 0.0000 0.0000
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