mewma.crit {spc}

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

l

smoothing parameter lambda of the MEWMA control chart.

L0

in-control ARL.

p

dimension of multivariate normal distribution.

hs

so-called headstart (enables fast initial response) – must be non-negative.

r

number of quadrature nodes – dimension of the resulting linear equation system.

Details

mewma.crit determines the alarm threshold of for given in-control ARL L0 by applying secant rule and using mewma.arl() with ntype="gl2".

Value

Returns a single value which resembles the critical value c.

Author(s)

Sven Knoth

References

Sven Knoth (2017), ARL Numerics for MEWMA Charts, 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, J. Stat. Comput. Simulation 52(4), 351-365.

See Also

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