Computation of the steady-state Average Run Length (ARL) for different types of EWMA control charts monitoring the mean of t distributed data.
xtewma.ad(l, c, df, mu1, mu0=0, zr=0, z0=0, sided="one", limits="fix",
steady.state.mode="conditional", mode="tan", r=40)Returns a single value which resembles the steady-state ARL.
smoothing parameter lambda of the EWMA control chart.
critical value (similar to alarm limit) of the EWMA control chart.
degrees of freedom -- parameter of the t distribution.
in-control mean.
out-of-control mean.
reflection border for the one-sided chart.
restarting value of the EWMA sequence in case of a false alarm in
steady.state.mode="cyclical".
distinguishes between one- and two-sided two-sided EWMA control
chart by choosing "one" and "two", respectively.
distinguishes between different control limits behavior.
distinguishes between two steady-state modes -- conditional and cyclical.
Controls the type of variables substitution that might improve the numerical performance. Currently,
"identity", "sin", "sinh", and "tan" (default) are provided.
number of quadrature nodes, dimension of the resulting linear
equation system is equal to r+1 (one-sided) or r
(two-sided).
Sven Knoth
xtewma.ad determines the steady-state Average Run Length (ARL)
by numerically solving the related ARL integral equation by means
of the Nystroem method based on Gauss-Legendre quadrature
and using the power method for deriving the largest in magnitude
eigenvalue and the related left eigenfunction.
R. B. Crosier (1986), A new two-sided cumulative quality control scheme, Technometrics 28, 187-194.
S. V. Crowder (1987), A simple method for studying run-length distributions of exponentially weighted moving average charts, Technometrics 29, 401-407.
J. M. Lucas and M. S. Saccucci (1990), Exponentially weighted moving average control schemes: Properties and enhancements, Technometrics 32, 1-12.
xtewma.arl for zero-state ARL computation and
xewma.ad for the steady-state ARL for normal data.