Elastic SPM Phase I Chart

Builds an SPM control chart that is invariant to phase (time-warping) variation. First aligns the functional data to a Karcher mean using elastic registration, then builds separate amplitude and (optionally) phase charts.

Usage

spm.elastic.phase1(
  fdataobj,
  ncomp = 5,
  alpha = 0.05,
  tuning.fraction = 0.5,
  seed = 42,
  align.lambda = 0,
  monitor.phase = TRUE,
  warp.ncomp = 3
)

Arguments

fdataobj

An object of class fdata with in-control data.

ncomp

Number of principal components for amplitude chart (default 5).

alpha

Significance level (default 0.05).

tuning.fraction

Fraction for FPCA tuning (default 0.5).

seed

Random seed (default 42).

align.lambda

Elastic alignment regularization (default 0.0).

monitor.phase

Logical; if TRUE, also builds a phase chart for warping function monitoring (default TRUE).

warp.ncomp

Number of components for the phase (warping) chart (default 3).

Value

An object of class spm.elastic.chart with components:

karcher.mean

The Karcher mean function

mean.alignment.residual

Residual from Karcher mean computation

amplitude

List with amplitude chart fields: eigenvalues, t2.phase1, spe.phase1, t2.ucl, spe.ucl, ncomp

phase

List with phase chart fields (if monitor.phase = TRUE), or NULL

fdataobj

Original fdata object

.rust

Internal fields for Phase II monitoring

See also

spm.elastic.monitor for Phase II elastic monitoring, spm.phase1 for non-elastic Phase I

Examples

# \donttest{
set.seed(1)
n <- 40; m <- 30
argvals <- seq(0, 1, length.out = m)
X <- matrix(rnorm(n * m), n, m)
fd <- fdata(X, argvals = argvals)

chart <- spm.elastic.phase1(fd, ncomp = 3, warp.ncomp = 2)
chart
#> Elastic SPM Control Chart (Phase I)
#>   Components (amplitude): 3 
#>   Alpha: 0.05 
#>   Amplitude T2 UCL: 7.815 
#>   Amplitude SPE UCL: 0.7933 
#>   Phase monitoring: enabled
#>   Phase components: 2 
#>   Phase T2 UCL: 5.991 
#>   Phase SPE UCL: 0.003706 
#>   Observations: 40 
#>   Grid points: 30 
# }