Simulate run lengths of a design — edetect

Estimates the average run length to a false alarm (ARL, no change) or the detection delay (with a change) of an e-detector design by Monte Carlo. The recursion is vectorised across replications.

Usage

edetect_arl(
  design,
  pre,
  post = NULL,
  change_at = 1L,
  n_rep = 200L,
  max_t = NULL
)

Arguments

design: An edetect_design().
pre: A function function(n) returning n pre-change observations (for the "bernoulli" and "poisson" classes, a data frame with columns x and n).
post: Optional function with the same signature for post-change observations. When supplied, the change happens at time change_at.
change_at: Time of the first post-change observation.
n_rep: Number of replications.
max_t: Censoring time; runs that have not alarmed by max_t are reported as censored.

Value

A list of class edetect_runs with runs (a tibble with one row per replication: run_length, alarm, delay when there is a change, false_alarm) and summary (a one-row tibble with the mean run length or delay, its standard error, the censoring fraction and, with a change, the false-alarm fraction before change_at).

Examples

design <- edetect_design(arl = 50, class = "subgaussian", center = 0, sigma = 1)
set.seed(1)
edetect_arl(design, pre = function(n) rnorm(n), n_rep = 50, max_t = 2000)$summary
#> # A tibble: 1 × 6
#>   arl_estimate    se censored target_arl n_rep max_t
#>          <dbl> <dbl>    <dbl>      <dbl> <int> <int>
#> 1         100.  12.3        0         50    50  2000
edetect_arl(design, pre = function(n) rnorm(n), post = function(n) rnorm(n, 1),
            change_at = 20, n_rep = 50, max_t = 500)$summary
#> # A tibble: 1 × 7
#>   delay_mean    se false_alarm censored change_at n_rep max_t
#>        <dbl> <dbl>       <dbl>    <dbl>     <int> <int> <int>
#> 1       5.48 0.362        0.08        0        20    50   500