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.
mewma.psi(l, cE, p, type="cond", hs=0, r=20)Returns a function.
smoothing parameter lambda of the MEWMA control chart.
alarm threshold of the MEWMA control chart.
dimension of multivariate normal distribution.
switch between "cond" and "cycl" for differentiating between the conditional
(no false alarm) and the cyclical (after false alarm re-start in hs), respectively.
the re-starting point for the cyclical steady-state framework.
number of quadrature nodes.
Sven Knoth
Basically, ideas from Knoth (2017, MEWMA numerics) and Knoth (2016, steady-state ARL concepts) are merged. More details will follow.
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.
mewma.arl for calculating the in-control ARL of MEWMA.
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
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