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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.
xcusum.crit.L0h(L0, h, hs=0, sided="one", r=30, L0.eps=1e-6, k.eps=1e-8)Returns a single value which resembles the reference value k.
in-control ARL.
alarm level of the CUSUM control chart.
so-called headstart (enables fast initial response).
distinguishes between one-, two-sided and Crosier's modified
two-sided CUSUM scheme choosing "one", "two", and "Crosier", respectively.
number of quadrature nodes, dimension of the resulting linear
equation system is equal to r+1 (one-, two-sided) or 2r+1 (Crosier).
error bound for the L0 error.
bound for the difference of two successive values of k.
Sven Knoth
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.
xcusum.arl for zero-state ARL computation.
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")
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