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\name{mewma.crit}
\alias{mewma.crit}
\title{Compute alarm threshold of MEWMA control charts}
\description{Computation of the alarm threshold for multivariate exponentially weighted
moving average (MEWMA) charts monitoring multivariate normal mean.}
\usage{mewma.crit(l, L0, p, hs=0, r=20)}
\arguments{
\item{l}{smoothing parameter lambda of the MEWMA control chart.}
\item{L0}{in-control ARL.}
\item{p}{dimension of multivariate normal distribution.}
\item{hs}{so-called headstart (enables fast initial response) -- must be non-negative.}
\item{r}{number of quadrature nodes -- dimension of the resulting linear equation system.}
}
\details{
\code{mewma.crit} determines the alarm threshold of for given in-control ARL \code{L0}
by applying secant rule and using \code{mewma.arl()} with \code{ntype="gl2"}.
}
\value{Returns a single value which resembles the critical value \code{c}.}
\references{
Sven Knoth (2017),
ARL Numerics for MEWMA Charts,
\emph{Journal of Quality Technology 49(1)}, 78-89.
Steven E. Rigdon (1995),
An integral equation for the in-control average run length of a multivariate exponentially weighted moving average control chart,
\emph{J. Stat. Comput. Simulation 52(4)}, 351-365.
}
\author{Sven Knoth}
\seealso{\code{mewma.arl} for zero-state ARL computation.}
\examples{
# Rigdon (1995), p. 358, Tab. 1
p <- 4
L0 <- 500
r <- .25
h4 <- mewma.crit(r, L0, p)
h4
## original value is 16.38.
# Knoth (2017), p. 82, Tab. 2
p <- 3
L0 <- 1e3
lambda <- c(0.25, 0.2, 0.15, 0.1, 0.05)
h4 <- rep(NA, length(lambda) )
for ( i in 1:length(lambda) ) h4[i] <- mewma.crit(lambda[i], L0, p, r=20)
round(h4, digits=2)
## original values are
## 15.82 15.62 15.31 14.76 13.60
}
\keyword{ts}
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