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# Computation of CUSUM k (reference value) for given in-control ARL and threshold h (mean monitoring)
xcusum.crit.L0h <- function(L0, h, hs=0, sided="one", r=30, L0.eps=1e-6, k.eps=1e-8) {
h.max <- xcusum.crit(0, L0, 0)
if ( h.max < h ) stop("h too large or L0 far too small")
k1 <- 0
L0_1 <- 0
while ( L0_1 < L0 ) {
k1 <- k1 + .1
L0_1 <- xcusum.arl(k1, h, 0, hs=hs, sided=sided, r=r)
}
while ( L0_1 > L0 & k1 > 0.01) {
k1 <- k1 - .01
L0_1 <- xcusum.arl(k1, h, 0, hs=hs, sided=sided, r=r)
}
k2 <- k1 + .01
L0_2 <- xcusum.arl(k2, h, 0, hs=hs, r=r)
dk <- 1
while ( abs(L0-L0_2) > L0.eps & abs(dk) > k.eps ) {
k3 <- k1 + ( L0 - L0_1 ) / ( L0_2 - L0_1 ) * ( k2 - k1 )
L0_3 <- xcusum.arl(k3, h, 0, hs=hs, sided=sided, r=r)
# secant rule
dk <- k3-k2
k1 <- k2
L0_1 <- L0_2
k2 <- k3
L0_2 <- L0_3
}
k3
}
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