spc (version 0.2.1)

sewma.arl: Compute ARLs of EWMA control charts (variance charts)

Description

Computation of the (zero-state) Average Run Length (ARL) for different types of EWMA control charts (based on the sample variance $S^2$) monitoring normal variance.

Usage

sewma.arl(l,cl,cu,sigma,df,s2.on=TRUE,hs=1,sided="upper",r=40,qm=30)

Arguments

l

smoothing parameter lambda of the EWMA control chart.

cl

lower control limit of the EWMA control chart.

cu

upper control limit of the EWMA control chart.

sigma

true standard deviation.

df

actual degrees of freedom, corresponds to batch size.

s2.on

distinguish between $S^2$ and $S$ chart.

hs

so-called headstart (give fast initial response).

sided

distinguish between one- and two-sided two-sided EWMA-$S^2$ control charts by choosing "upper" (upper chart without reflection at cl -- the actual value of cl is not used), "Rupper" (upper chart with r

r

dimension of the resulting linear equation system.

qm

number of quadrature nodes.

Value

• Returns a single value which resembles the ARL.

Details

sewma.arl determines the Average Run Length (ARL) by numerically solving the related ARL integral equation by means of collocation (Chebyshev polynomials).

References

S. Knoth (2005), Accurate ARL computation for EWMA-$S^2$ control charts, Statistics and Computing 15, 341-352.

See Also

xewma.arl for zero-state ARL computation of EWMA control charts for monitoring normal mean.

Examples

## Knoth (2005)
## compare with Table 1 (p. 347): 249.9997
## Monte Carlo with 10^9 replicates: 249.9892 +/- 0.008
l <- .025
df <- 1
cu <- 1 + 1.661865*sqrt(l/(2-l))*sqrt(2/df) 
sewma.arl(l,0,cu,1,df)