xgrsr.crit {spc}

Compute alarm thresholds for Shiryaev-Roberts schemes

Description

Computation of the alarm thresholds (alarm limits) for Shiryaev-Roberts schemes monitoring normal mean.

Usage

xgrsr.crit(k, L0, mu0 = 0, zr = 0, hs = NULL, sided = "one", MPT = FALSE, r = 30)

Arguments

k

reference value of the Shiryaev-Roberts scheme.

L0

in-control ARL.

mu0

in-control mean.

zr

reflection border to enable the numerical algorithms used here.

hs

so-called headstart (enables fast initial response). If hs=NULL, then the classical headstart -Inf is used (corresponds to 0 for the non-log scheme).

sided

distinguishes between one- and two-sided schemes by choosing "one" and"two", respectively. Currently only one-sided schemes are implemented.

MPT

switch between the old implementation (FALSE) and the new one (TRUE) that considers the completed likelihood ratio. MPT contains the initials of G. Moustakides, A. Polunchenko and A. Tartakovsky.

r

number of quadrature nodes, dimension of the resulting linear equation system is equal to r+1.

Details

xgrsr.crit determines the alarm threshold (alarm limit) for given in-control ARL L0 by applying secant rule and using xgrsr.arl().

Value

Returns a single value which resembles the alarm limit g.

Author(s)

Sven Knoth

References

G. Moustakides, A. Polunchenko, A. Tartakovsky (2009), Numerical comparison of CUSUM and Shiryaev-Roberts procedures for detecting changes in distributions, Communications in Statistics: Theory and Methods 38, 3225-3239.r.

See Also

xgrsr.arl for zero-state ARL computation.

Examples

## Table 4 from Moustakides et al. (2009)
## original values are
# gamma/L0  A/exp(g)
# 50        28.02
# 100       56.04
# 500       280.19
# 1000      560.37
# 5000      2801.75
# 10000     5603.7
theta <- 1
zr <- -6
r <- 100
Lxgrsr.crit  <- Vectorize("xgrsr.crit", "L0")
L0s <- c(50, 100, 500, 1000, 5000, 10000)
gs <- Lxgrsr.crit(theta/2, L0s, zr=zr, r=r)
data.frame(L0s, gs, A=round(exp(gs), digits=2))