mewma.crit: Compute alarm threshold of MEWMA control charts

In spc: Statistical Process Control -- Calculation of ARL and Other Control Chart Performance Measures

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

spc documentation built on Oct. 24, 2022, 5:07 p.m.