xcusum.crit.L0h {spc}

Compute the CUSUM reference value k for given in-control ARL and threshold h

Description

Computation of the reference value k for one-sided CUSUM control charts monitoring normal mean, if the in-control ARL L0 and the alarm threshold h are given.

Usage

xcusum.crit.L0h(L0, h, hs=0, sided="one", r=30, L0.eps=1e-6, k.eps=1e-8)

Arguments

L0

in-control ARL.

h

alarm level of the CUSUM control chart.

hs

so-called headstart (enables fast initial response).

sided

distinguishes between one-, two-sided and Crosier's modified two-sided CUSUM scheme choosing "one", "two", and "Crosier", respectively.

r

number of quadrature nodes, dimension of the resulting linear equation system is equal to r+1 (one-, two-sided) or 2r+1 (Crosier).

L0.eps

error bound for the L0 error.

k.eps

bound for the difference of two successive values of k.

Details

xcusum.crit.L0h determines the reference value k for given in-control ARL L0 and alarm level h by applying secant rule and using xcusum.arl(). Note that not for any combination of L0 and h a solution exists – for given L0 there is a maximal value for h to get a valid result k.

Value

Returns a single value which resembles the reference value k.

Author(s)

Sven Knoth

See Also

xcusum.arl for zero-state ARL computation.

Examples

L0 <- 100
h.max <- xcusum.crit(0, L0, 0)
hs <- (300:1)/100
hs <- hs[hs < h.max]
ks <- NULL
for ( h in hs ) ks <- c(ks, xcusum.crit.L0h(L0, h))  
k.max <- qnorm( 1 - 1/L0 )
plot(hs, ks, type="l", ylim=c(0, max(k.max, ks)), xlab="h", ylab="k")
abline(h=c(0, k.max), col="red")