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Adaptive MEWMA (AMEWMA) Monitoring for Functional Data

Source: R/spm.R
spm.amewma.Rd

Applies Adaptive Multivariate EWMA monitoring where the smoothing parameter adapts over time based on the magnitude of recent deviations. This provides good detection performance for both small and large shifts.

Usage

spm.amewma(
  chart,
  newdata,
  lambda.min = 0.05,
  lambda.max = 0.95,
  lambda.init = 0.2,
  eta = 0.1,
  ncomp = NULL,
  alpha = 0.05
)

Arguments

chart

An object of class spm.chart from spm.phase1.

newdata

An object of class fdata with sequential observations.

lambda.min

Minimum smoothing parameter (default 0.05).

lambda.max

Maximum smoothing parameter (default 0.95).

lambda.init

Initial smoothing parameter (default 0.2).

eta

Learning rate for lambda adaptation (default 0.1).

ncomp

Number of components (default: same as chart).

alpha

Significance level (default 0.05).

Value

An object of class spm.amewma with components:

smoothed.scores

Matrix of adaptively smoothed score vectors

t2.statistic

Numeric vector of T-squared statistics on smoothed scores

lambda.t

Numeric vector of adaptive lambda values over time

ucl

Control limit

alarm

Logical vector: TRUE where statistic exceeds UCL

See also

spm.mewma for fixed-lambda MEWMA, spm.ewma for univariate EWMA

Examples

# \donttest{
set.seed(1)
n <- 50; m <- 30
argvals <- seq(0, 1, length.out = m)
X <- matrix(rnorm(n * m), n, m)
fd <- fdata(X, argvals = argvals)
chart <- spm.phase1(fd, ncomp = 3)

X_new <- matrix(rnorm(30 * m) + 0.5, 30, m)
fd_new <- fdata(X_new, argvals = argvals)
amewma <- spm.amewma(chart, fd_new)
amewma
#> SPM Adaptive MEWMA (AMEWMA) Monitoring
#>   Observations: 30 
#>   Lambda range: [0.05, 0.95]
#>   Lambda init: 0.2 
#>   Eta: 0.1 
#>   UCL: 7.815 
#>   Alarms: 0 of 30 (0%) 
# }