Trace-Statistic Control Chart — cchart.trV • IQCC

Construct and optionally plot a Shewhart-type upper control chart for multivariate process variability using the standardized trace statistic \(tr(V)\).

Usage

cchart.trV(
  x,
  size = NULL,
  Sigma0 = NULL,
  alpha = 0.0027,
  type = c("chisq", "simulation"),
  nsim = 1e+05,
  seed = NULL,
  newdata = NULL,
  plot = TRUE,
  ...
)

# S3 method for class 'cchart.trV'
plot(x, ...)

# S3 method for class 'cchart.trV'
print(x, digits = max(3L, getOption("digits") - 3L), ...)

# S3 method for class 'cchart.trV'
summary(object, ...)

# S3 method for class 'summary.cchart.trV'
print(x, digits = max(3L, getOption("digits") - 3L), ...)

Arguments

x

An object of class "summary.cchart.trV".

size

Positive integer subgroup size when x or newdata is a stacked matrix.

Sigma0

Optional finite symmetric positive-definite in-control covariance matrix. If omitted, the average Phase I covariance matrix is used as a plug-in estimate.

alpha

Nominal upper-tail false-alarm probability, strictly between 0 and 1.

type

Character string selecting the calculation:

"chisq": Exact chi-square quantile with \(p(n - 1)\) degrees of freedom.
"simulation": Monte Carlo quantile from the same chi-square distribution. This is mainly a diagnostic and teaching option.

nsim

Integer number of Monte Carlo draws, at least 1000. Used only when type = "simulation".

seed

NULL or a finite numeric scalar used as the Monte Carlo seed. A supplied seed makes simulated limits reproducible and restores the caller's existing random-number state on exit.

newdata

Optional Phase II subgroup data in any format accepted by trv_stat. Phase II subgroups must have the same subgroup size and dimension as Phase I.

plot

Logical scalar. If TRUE, draw the chart before returning the result.

...

Currently unused.

digits

Number of significant digits used for numerical output.

object

An object of class "cchart.trV".

Value

An object of class "cchart.trV", a list with components:

statistics: Trace statistics for all Phase I followed by all Phase II subgroups.
phase1, phase2: Integer indices identifying the two phases in statistics.
limits: The complete list returned by trv_limits().
out.of.control: Indices for which statistics > ucl. Equality to the limit does not signal.
Sigma0: The supplied or estimated in-control covariance matrix.
Sbar: The average Phase I covariance matrix when Sigma0 is estimated, otherwise NULL.
n, p: Subgroup size and process dimension.
call: The matched function call.

For plot.cchart.trV(), x invisibly.

x, invisibly.

An object of class "summary.cchart.trV".

x, invisibly.

Details

The tr(V) chart complements cchart.GV. The generalized variance chart monitors determinant changes, while the trace chart monitors the sum of standardized covariance eigenvalues. When Sigma0 = NULL, limits are plug-in limits conditional on the Phase I estimate and do not include additional Phase I estimation uncertainty.

Examples

set.seed(123)
phase1 <- array(rnorm(6 * 8 * 2), dim = c(6, 8, 2))
chart <- cchart.trV(phase1, Sigma0 = diag(2), plot = FALSE)
chart$limits[c("center", "ucl")]
#> $center
#> [1] 14
#> 
#> $ucl
#> [1] 33.19518
#>