xewma.sf | R Documentation |
Computation of the survival function of the Run Length (RL) for EWMA control charts monitoring normal mean.
xewma.sf(l, c, mu, n, zr=0, hs=0, sided="one", limits="fix", q=1, r=40)
l |
smoothing parameter lambda of the EWMA control chart. |
c |
critical value (similar to alarm limit) of the EWMA control chart. |
mu |
true mean. |
n |
calculate sf up to value |
zr |
reflection border for the one-sided chart. |
hs |
so-called headstart (enables fast initial response). |
sided |
distinguishes between one- and two-sided EWMA control chart
by choosing |
limits |
distinguishes between different control limits behavior. |
q |
change point position. For |
r |
number of quadrature nodes, dimension of the resulting linear
equation system is equal to |
The survival function P(L>n) and derived from it also the cdf P(L<=n) and the pmf P(L=n) illustrate
the distribution of the EWMA run length. For large n the geometric tail could be exploited. That is,
with reasonable large n the complete distribution is characterized.
The algorithm is based on Waldmann's survival function iteration procedure.
For varying limits and for change points after 1 the algorithm from Knoth (2004) is applied.
Note that for one-sided EWMA charts (sided
="one"
), only
"vacl"
and "stat"
are deployed, while for two-sided ones
(sided
="two"
) also "fir"
, "both"
(combination of "fir"
and "vacl"
), and "Steiner"
are implemented.
For details see Knoth (2004).
Returns a vector which resembles the survival function up to a certain point.
Sven Knoth
F. F. Gan (1993), An optimal design of EWMA control charts based on the median run length, J. Stat. Comput. Simulation 45, 169-184.
S. Knoth (2003), EWMA schemes with non-homogeneous transition kernels, Sequential Analysis 22, 241-255.
S. Knoth (2004), Fast initial response features for EWMA Control Charts, Statistical Papers 46, 47-64.
K.-H. Waldmann (1986), Bounds for the distribution of the run length of geometric moving average charts, Appl. Statist. 35, 151-158.
xewma.arl
for zero-state ARL computation of EWMA control charts.
## Gan (1993), two-sided EWMA with fixed control limits
## some values of his Table 1 -- any median RL should be 500
G.lambda <- c(.05, .1, .15, .2, .25)
G.h <- c(.441, .675, .863, 1.027, 1.177)/sqrt(G.lambda/(2-G.lambda))
for ( i in 1:length(G.lambda) ) {
SF <- xewma.sf(G.lambda[i], G.h[i], 0, 1000)
if (i==1) plot(1:length(SF), SF, type="l", xlab="n", ylab="P(L>n)")
else lines(1:length(SF), SF, col=i)
}
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