xtewma.ad {spc}

Compute steady-state ARLs of EWMA control charts, t distributed data

Description

Computation of the steady-state Average Run Length (ARL) for different types of EWMA control charts monitoring the mean of t distributed data.

Usage

xtewma.ad(l, c, df, mu1, mu0=0, zr=0, z0=0, sided="one", limits="fix",
steady.state.mode="conditional", mode="tan", r=40)

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.

mu1

in-control mean.

mu0

out-of-control mean.

zr

reflection border for the one-sided chart.

z0

restarting value of the EWMA sequence in case of a false alarm in steady.state.mode="cyclical".

sided

distinguishes between one- and two-sided two-sided EWMA control chart by choosing "one" and "two", respectively.

limits

distinguishes between different control limits behavior.

steady.state.mode

distinguishes between two steady-state modes – conditional and cyclical.

mode

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

r

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

Details

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.

Value

Returns a single value which resembles the steady-state ARL.

Author(s)

Sven Knoth

References

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.

See Also

xtewma.arl for zero-state ARL computation and xewma.ad for the steady-state ARL for normal data.

Examples

## will follow