xtewma.q {spc}

Compute RL quantiles of EWMA control charts

Description

Computation of quantiles of the Run Length (RL) for EWMA control charts monitoring normal mean.

Usage

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)

Arguments

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.

alpha

quantile level.

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 "one" and "two", respectively.

limits

distinguishes between different control limits behavior.

mode

Controls the type of variables substitution that might improve the numerical performance. Currently, "identity", "sin", "sinh", and "tan" (default) are provided.

q

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.

r

number of quadrature nodes, dimension of the resulting linear equation system is equal to r+1 (one-sided) or r (two-sided).

L0

in-control quantile value.

c.error

error bound for two succeeding values of the critical value during applying the secant rule.

a.error

error bound for the quantile level alpha during applying the secant rule.

OUTPUT

activate or deactivate additional output.

Details

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).

Value

Returns a single value which resembles the RL quantile of order q.

Author(s)

Sven Knoth

References

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.

See Also

xewma.q for RL quantile computation of EWMA control charts in the normal case.

Examples

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