xtewma.sf | R Documentation |
Computation of the survival function of the Run Length (RL) for EWMA control charts monitoring normal mean.
xtewma.sf(l, c, df, mu, n, zr=0, hs=0, sided="two", limits="fix", mode="tan", 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. |
df |
degrees of freedom – parameter of the t distribution. |
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 conrol limits behavior. |
mode |
Controls the type of variables substitution that might improve the numerical performance. Currently,
|
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. 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.sf
for survival function computation of EWMA control charts in the normal case.
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