CUSUM Monitoring for Functional Data

Applies Cumulative Sum (CUSUM) monitoring to sequential functional data. CUSUM accumulates evidence of a mean shift over time, providing faster detection of small persistent shifts than Shewhart-type charts.

Usage

spm.cusum(
  chart,
  newdata,
  k = 0.5,
  h = 5,
  ncomp = NULL,
  alpha = 0.05,
  restart = FALSE
)

Arguments

chart

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

newdata

An object of class fdata with sequential observations.

k

CUSUM allowance (slack) parameter (default 0.5). Controls the size of shift the CUSUM is tuned to detect.

h

CUSUM decision interval (default 5.0). Larger values give fewer false alarms but slower detection.

ncomp

Number of components for CUSUM (default: same as chart).

alpha

Significance level for SPE limit (default 0.05).

restart

Logical; if TRUE, the CUSUM resets to zero after each alarm (default FALSE).

Value

An object of class spm.cusum with components:

cusum.statistic

Numeric vector of CUSUM values

ucl

Decision interval (h)

alarm

Logical vector: TRUE where CUSUM exceeds h

scores

FPC score matrix

spe

SPE values

spe.limit

SPE control limit

spe.alarm

Logical: TRUE where SPE exceeds limit

See also

spm.monitor for Shewhart-type monitoring, spm.mewma for MEWMA monitoring

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)

# Monitor with a small persistent shift
X_new <- matrix(rnorm(30 * m) + 0.5, 30, m)
fd_new <- fdata(X_new, argvals = argvals)
cusum <- spm.cusum(chart, fd_new, k = 0.5, h = 5.0)
cusum
#> SPM CUSUM Monitoring
#>   Observations: 30 
#>   k: 0.5 
#>   h (UCL): 5 
#>   Restart: FALSE 
#>   CUSUM alarms: 22 of 30 (73.3%) 
#>   SPE alarms: 2 of 30 (6.67%) 
# }