xewma.crit: Compute critical values of EWMA control charts

In spc: Statistical Process Control -- Calculation of ARL and Other Control Chart Performance Measures

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)

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.

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.

spc documentation built on Oct. 24, 2022, 5:07 p.m.