False-Alarm Risk for Trace-Statistic Charts

Evaluate the actual in-control upper-tail probability of a supplied tr(V) upper control limit.

Usage

trv_alpha_risk(
  n,
  p,
  ucl,
  Sigma0 = NULL,
  type = c("chisq", "simulation"),
  nsim = 1e+05,
  seed = NULL
)

Arguments

n

Integer subgroup sample size, at least 2.

p

Integer process dimension, at least 2.

ucl

Positive finite upper control limit on the trace statistic.

Sigma0

Optional in-control covariance matrix. It is accepted for API symmetry with trv_stat and validated when supplied, but the null distribution of the standardized trace statistic depends only on n and p.

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.

Value

A list with components alpha, arl0, ucl, n, p, df, and method.

Examples

lim <- trv_limits(8, 2)
trv_alpha_risk(8, 2, lim$ucl)
#> $alpha
#> [1] 0.0027
#> 
#> $arl0
#> [1] 370.3704
#> 
#> $ucl
#> [1] 33.19518
#> 
#> $n
#> [1] 8
#> 
#> $p
#> [1] 2
#> 
#> $df
#> [1] 14
#> 
#> $method
#> [1] "exact chi-square"
#>