xsewma.sf | R Documentation |
Computation of the survival function of the Run Length (RL) for EWMA control charts monitoring simultaneously normal mean and variance.
xsewma.sf(n, lx, cx, ls, csu, df, mu, sigma, hsx=0, Nx=40,
csl=0, hss=1, Ns=40, sided="upper", qm=30)
n |
calculate sf up to value |
lx |
smoothing parameter lambda of the two-sided mean EWMA chart. |
cx |
control limit of the two-sided mean EWMA control chart. |
ls |
smoothing parameter lambda of the variance EWMA chart. |
csu |
upper control limit of the variance EWMA control chart. |
df |
actual degrees of freedom, corresponds to subgroup size (for known mean it is equal to the subgroup size, for unknown mean it is equal to subgroup size minus one. |
mu |
true mean. |
sigma |
true standard deviation. |
hsx |
so-called headstart (enables fast initial response) of the mean chart – do not confuse with the true FIR feature considered in xewma.arl; will be updated. |
Nx |
dimension of the approximating matrix of the mean chart. |
csl |
lower control limit of the variance EWMA control chart; default value is 0;
not considered if |
hss |
headstart (enables fast initial response) of the variance chart. |
Ns |
dimension of the approximating matrix of the variance chart. |
sided |
distinguishes between one- and two-sided two-sided
EWMA- |
qm |
number of quadrature nodes used for the collocation integrals. |
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 and on results in Knoth (2007).
Returns a vector which resembles the survival function up to a certain point.
Sven Knoth
S. Knoth (2007), Accurate ARL calculation for EWMA control charts monitoring simultaneously normal mean and variance, Sequential Analysis 26, 251-264.
K.-H. Waldmann (1986), Bounds for the distribution of the run length of geometric moving average charts, Appl. Statist. 35, 151-158.
xsewma.arl
for zero-state ARL computation of simultaneous EWMA
control charts.
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