Skip to contents

Estimate Average Run Length (ARL)

Source: R/spm.R
spm.arl.Rd

Estimates the Average Run Length (ARL) for a T-squared or SPE control chart via Monte Carlo simulation. In-control ARL (shift.magnitude = NULL) measures the expected number of observations before a false alarm. Out-of-control ARL measures detection speed under a mean shift.

Usage

spm.arl(
  chart,
  type = c("t2", "spe"),
  shift.magnitude = NULL,
  n.sim = 10000,
  max.rl = 5000,
  seed = 42
)

Arguments

chart

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

type

Which statistic: "t2" or "spe".

shift.magnitude

For out-of-control ARL: numeric vector of per-component shifts (length = ncomp). If NULL, computes in-control ARL.

n.sim

Number of Monte Carlo simulations (default 10000).

max.rl

Maximum run length per simulation (default 5000).

seed

Random seed (default 42).

Value

An object of class spm.arl with components:

arl

Estimated ARL

std.dev

Standard deviation of run lengths

median.rl

Median run length

run.lengths

Integer vector of all simulated run lengths

type

Which statistic was used

in.control

Logical: TRUE if in-control ARL

See also

spm.arl.ewma for EWMA-based ARL

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)

# In-control ARL
arl0 <- spm.arl(chart, type = "t2", n.sim = 1000)
arl0
#> SPM Average Run Length (In-Control)
#>   Statistic: T2 
#>   ARL: 19.62 
#>   Std. Dev.: 19.02 
#>   Median RL: 14 
#>   Simulations: 1000 
# }