mewma.psi {spc}

Compute steady-state density of the MEWMA statistic

Description

Computation of the (zero-state) steady-state density function of the statistic deployed in multivariate exponentially weighted moving average (MEWMA) charts monitoring multivariate normal mean.

Usage

mewma.psi(l, cE, p, type="cond", hs=0, r=20)

Arguments

l

smoothing parameter lambda of the MEWMA control chart.

cE

alarm threshold of the MEWMA control chart.

p

dimension of multivariate normal distribution.

type

switch between "cond" and "cycl" for differentiating between the conditional (no false alarm) and the cyclical (after false alarm re-start in hs), respectively.

hs

the re-starting point for the cyclical steady-state framework.

r

number of quadrature nodes.

Details

Basically, ideas from Knoth (2017, MEWMA numerics) and Knoth (2016, steady-state ARL concepts) are merged. More details will follow.

Value

Returns a function.

Author(s)

Sven Knoth

References

Sven Knoth (2016), The Case Against the Use of Synthetic Control Charts, Journal of Quality Technology 48(2), 178-195.

Sven Knoth (2017), ARL Numerics for MEWMA Charts, Journal of Quality Technology 49(1), 78-89.

Sven Knoth (2018), The Steady-State Behavior of Multivariate Exponentially Weighted Moving Average Control Charts, Sequential Analysis 37(4), 511-529.

See Also

mewma.arl for calculating the in-control ARL of MEWMA.

Examples

lambda <- 0.1
L0 <- 200
p <- 3
h4 <- mewma.crit(lambda, L0, p)
x_ <- seq(0, h4*lambda/(2-lambda), by=0.002)
psi <- mewma.psi(lambda, h4, p)
psi_ <- psi(x_)
# plot(x_, psi_, type="l", xlab="x", ylab=expression(psi(x)), xlim=c(0,1.2))
# cf. to Figure 1 in Knoth (2018), p. 514, p=3