xDshewhartrunsrules.arl {spc} | R Documentation |
Compute ARLs of Shewhart control charts with and without runs rules under drift
Description
Computation of the zero-state Average Run Length (ARL) under drift for Shewhart control charts with and without runs rules monitoring normal mean.
Usage
xDshewhartrunsrules.arl(delta, c = 1, m = NULL, type = "12")
xDshewhartrunsrulesFixedm.arl(delta, c = 1, m = 100, type = "12")
Arguments
delta |
true drift parameter. |
c |
normalizing constant to ensure specific alarming behavior. |
type |
controls the type of Shewhart chart used, seed details section. |
m |
parameter of Gan's approach. If |
Details
Based on Gan (1991), the ARL is calculated for
Shewhart control charts with and without runs rules
under drift. The usual ARL function with mu=m*delta is determined and recursively via
m-1, m-2, ... 1 (or 0) the drift ARL determined.
xDshewhartrunsrulesFixedm.arl
is the actual work horse, while
xDshewhartrunsrules.arl
provides a convenience wrapper.
Note that Aerne et al. (1991) deployed a method that is
quite similar to Gan's algorithm. For type
see
the help page of xshewhartrunsrules.arl
.
Value
Returns a single value which resembles the ARL.
Author(s)
Sven Knoth
References
F. F. Gan (1991), EWMA control chart under linear drift, J. Stat. Comput. Simulation 38, 181-200.
L. A. Aerne, C. W. Champ and S. E. Rigdon (1991), Evaluation of control charts under linear trend, Commun. Stat., Theory Methods 20, 3341-3349.
See Also
xshewhartrunsrules.arl
for zero-state ARL computation of
Shewhart control charts with and without runs rules
for the classical step change model.
Examples
## Aerne et al. (1991)
## Table I (continued)
## original numbers are
# delta arl1of1 arl2of3 arl4of5 arl10
# 0.005623 136.67 120.90 105.34 107.08
# 0.007499 114.98 101.23 88.09 89.94
# 0.010000 96.03 84.22 73.31 75.23
# 0.013335 79.69 69.68 60.75 62.73
# 0.017783 65.75 57.38 50.18 52.18
# 0.023714 53.99 47.06 41.33 43.35
# 0.031623 44.15 38.47 33.99 36.00
# 0.042170 35.97 31.36 27.91 29.90
# 0.056234 29.21 25.51 22.91 24.86
# 0.074989 23.65 20.71 18.81 20.70
# 0.100000 19.11 16.79 15.45 17.29
# 0.133352 15.41 13.61 12.72 14.47
# 0.177828 12.41 11.03 10.50 12.14
# 0.237137 9.98 8.94 8.71 10.18
# 0.316228 8.02 7.25 7.26 8.45
# 0.421697 6.44 5.89 6.09 6.84
# 0.562341 5.17 4.80 5.15 5.48
# 0.749894 4.16 3.92 4.36 4.39
# 1.000000 3.35 3.22 3.63 3.52
c1of1 <- 3.069/3
c2of3 <- 2.1494/2
c4of5 <- 1.14
c10 <- 3.2425/3
DxDshewhartrunsrules.arl <- Vectorize(xDshewhartrunsrules.arl, "delta")
deltas <- 10^(-(18:0)/8)
arl1of1 <-
round(DxDshewhartrunsrules.arl(deltas, c=c1of1, type="1"), digits=2)
arl2of3 <-
round(DxDshewhartrunsrules.arl(deltas, c=c2of3, type="12"), digits=2)
arl4of5 <-
round(DxDshewhartrunsrules.arl(deltas, c=c4of5, type="13"), digits=2)
arl10 <-
round(DxDshewhartrunsrules.arl(deltas, c=c10, type="SameSide10"), digits=2)
data.frame(delta=round(deltas, digits=6), arl1of1, arl2of3, arl4of5, arl10)