EWMA-Based SPM Monitoring

Applies Exponentially Weighted Moving Average (EWMA) smoothing to FPC scores before computing monitoring statistics. This increases sensitivity to small persistent shifts in the process.

Usage

spm.ewma(chart, newdata, lambda = 0.2, 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 (rows in time order).

lambda

EWMA smoothing parameter in (0, 1] (default 0.2). Smaller values give more smoothing; lambda = 1 gives raw scores.

ncomp

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

alpha

Significance level for EWMA control limit (default 0.05).

Value

A list with components:

smoothed.scores

EWMA-smoothed score matrix

t2

T-squared values on smoothed scores

spe

SPE values (unsmoothed)

t2.limit

T-squared control limit for EWMA

spe.limit

SPE control limit

t2.alarm

Logical: TRUE where T-squared exceeds limit

spe.alarm

Logical: TRUE where SPE exceeds limit

See also

spm.phase1 for building the chart, spm.monitor for standard (non-EWMA) 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)

# Sequential monitoring with small shift
X_seq <- matrix(rnorm(20 * m) + 0.5, 20, m)
fd_seq <- fdata(X_seq, argvals = argvals)
ewma_result <- spm.ewma(chart, fd_seq, lambda = 0.2)
ewma_result$t2.alarm
#>  [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
#> [13] FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE
# }