xewma.crit {spc}

Compute critical values of EWMA control charts

Description

Computation of the critical values (similar to alarm limits) for different types of EWMA control charts monitoring normal mean.

Usage

xewma.crit(l,L0,mu0=0,zr=0,hs=0,sided="one",limits="fix",r=40,c0=NULL,nmax=10000)

Arguments

l

smoothing parameter lambda of the EWMA control chart.

L0

in-control ARL.

mu0

in-control mean.

zr

reflection border for the one-sided chart.

hs

so-called headstart (enables fast initial response).

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.

r

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

c0

starting value for iteration rule.

nmax

maximum number of individual control limit factors for "cfar".

Details

xewma.crit determines the critical values (similar to alarm limits) for given in-control ARL L0 by applying secant rule and using xewma.arl().

Value

Returns a single value which resembles the critical value c.

Author(s)

Sven Knoth

References

S. V. Crowder (1989), Design of exponentially weighted moving average schemes, Journal of Quality Technology 21, 155-162.

See Also

xewma.arl for zero-state ARL computation.

Examples

l <- .1
incontrolARL <- c(500,5000,50000)
sapply(incontrolARL,l=l,sided="two",xewma.crit,r=35) # accuracy with 35 nodes
sapply(incontrolARL,l=l,sided="two",xewma.crit)      # accuracy with 40 nodes
sapply(incontrolARL,l=l,sided="two",xewma.crit,r=50) # accuracy with 50 nodes

## Crowder (1989)
## two-sided EWMA control charts with fixed limits

l <- c(.05,.1,.15,.2,.25)
L0 <- 250
round(sapply(l,L0=L0,sided="two",xewma.crit),digits=2)

## original values are 2.32, 2.55, 2.65, 2.72, and 2.76.