Computation of quantiles of the Run Length (RL) for EWMA control charts monitoring normal mean.
xtewma.q(l, c, df, mu, alpha, zr=0, hs=0, sided="two", limits="fix", mode="tan",
q=1, r=40)xtewma.q.crit(l, L0, df, mu, alpha, zr=0, hs=0, sided="two", limits="fix", mode="tan",
r=40, c.error=1e-12, a.error=1e-9, OUTPUT=FALSE)
Returns a single value which resembles the RL quantile of order q.
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.
true mean.
quantile level.
reflection border for the one-sided chart.
so-called headstart (enables fast initial response).
distinguishes between one- and two-sided EWMA control chart
by choosing "one" and "two", respectively.
distinguishes between different control limits behavior.
Controls the type of variables substitution that might improve the numerical performance. Currently,
"identity", "sin", "sinh", and "tan" (default) are provided.
change point position. For \(q=1\) and \(\mu=\mu_0\) and \(\mu=\mu_1\), the usual zero-state ARLs for the in-control and out-of-control case, respectively, are calculated. For \(q>1\) and \(\mu!=0\) conditional delays, that is, \(E_q(L-q+1|L\geq)\), will be determined. Note that mu0=0 is implicitely fixed.
number of quadrature nodes, dimension of the resulting linear
equation system is equal to r+1 (one-sided) or r
(two-sided).
in-control quantile value.
error bound for two succeeding values of the critical value during applying the secant rule.
error bound for the quantile level alpha during applying
the secant rule.
activate or deactivate additional output.
Sven Knoth
Instead of the popular ARL (Average Run Length) quantiles of the EWMA
stopping time (Run Length) are determined. The algorithm is based on
Waldmann's survival function iteration procedure.
If limits is "vacl", then the method presented in Knoth (2003) is utilized.
For details see Knoth (2004).
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.q for RL quantile computation of EWMA control charts in the normal case.