Package 'edetect'

Plot a detector

Description

Two panels: the observations (as values, proportions or rates per unit exposure) with the pre-change centre, and the evidence of the detector on the log10 scale with the alarm threshold and, if any, the alarm time and the estimated change point.

Usage

## S3 method for class 'edetect_chart'
autoplot(object, ...)

Arguments

object	An edetect_chart.
...	Unused.

Value

A ggplot.

Examples

chart <- edetect_c(x = c(3, 2, 4, 3, 8, 9, 11, 10), center = 3, arl = 100)
autoplot(chart)

---

The alarm status of a detector

Description

The alarm status of a detector

Usage

edetect_alarm(state)

Arguments

state

An edetect_chart.

Value

A one-row tibble with alarm (logical), alarm_time, evidence at the alarm (or the current evidence), threshold, change_estimate (the start of the e-process that carries most of the current evidence) and n_observed.

Examples

design <- edetect_design(arl = 100, class = "subgaussian", center = 0, sigma = 1)
state <- edetect_update(edetect_init(design), rnorm(10))
edetect_alarm(state)

---

Simulate run lengths of a design

Description

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)$summary
edetect_arl(design, pre = function(n) rnorm(n), post = function(n) rnorm(n, 1),
            change_at = 20, n_rep = 50, max_t = 500)$summary

---

c chart: counts of nonconformities per unit

Description

c chart: counts of nonconformities per unit

Usage

edetect_c(x, center = NULL, phase1 = NULL, ...)

Arguments

x	Counts per inspection unit.
center	Pre-change mean count; omit to estimate it from phase1.
phase1	Optional Phase I counts (a numeric vector, unit exposure).
...	Passed to edetect_design() (arl, direction, type, evalue, delta, weights).

Value

An edetect_chart.

Examples

chart <- edetect_c(x = c(3, 2, 4, 3, 8, 9, 11), center = 3, arl = 100)
edetect_alarm(chart)

---

Pre-change classes

Description

The classes of pre-change distributions for which edetect builds e-values. Each class is a statement about the observations before a change; the average run length guarantee holds for every distribution in the class.

Usage

edetect_classes()

Details

• "bounded": observations in known bounds ⁠[a, b]⁠ with mean at most (direction "up"), at least ("down") or equal to ("both") center. Nothing else is assumed. E-values: "betting" (tight, default) or "hoeffding" (sub-Bernoulli).

• "subgaussian": observations with mean center and sub-Gaussian tails with declared scale sigma. Gaussian data with standard deviation sigma is the boundary case; heavier tails violate the class.

• "bernoulli": counts of successes in subgroups of size n, each trial with conditional success probability (given the earlier trials of the subgroup) at most/at least/equal to center; beyond that, dependence within a subgroup is allowed. This is the p chart.

• "poisson": counts with exposure n whose moment generating function is at most that of a Poisson with rate center per unit exposure (Poisson and underdispersed counts; overdispersed counts violate the class). These are the c (n = 1) and u charts.

Value

A character vector of class names.

Examples

edetect_classes()

---

Design an e-detector

Description

Fixes, before any Phase II observation is seen, everything the detector needs: the pre-change class and its parameters, the direction of the change to detect, the detector type (Shiryaev–Roberts or CUSUM), the family of e-values and the mixture over post-change alternatives, and the target average run length (ARL) to a false alarm.

Usage

edetect_design(
  arl = 370,
  class = edetect_classes(),
  center = NULL,
  bounds = NULL,
  sigma = NULL,
  direction = c("up", "down", "both"),
  type = c("sr", "cusum"),
  evalue = c("betting", "hoeffding"),
  delta = NULL,
  weights = NULL,
  phase1 = NULL
)

Arguments

arl	Target average run length to a false alarm. The alarm threshold is arl on the e-detector scale (equivalently alpha = 1 / arl).
class	Pre-change class, see edetect_classes().
center	Pre-change mean ("bounded", "subgaussian"), success probability ("bernoulli") or rate per unit exposure ("poisson"). May be omitted when phase1 is supplied.
bounds	Known bounds c(a, b) of the observations ("bounded" only).
sigma	Declared sub-Gaussian scale ("subgaussian" only). May be omitted when phase1 is supplied, in which case the Phase I standard deviation is used and recorded as an assumption.
direction	Change to detect: an increase ("up"), a decrease ("down") or either ("both", a half-and-half mixture of the two).
type	"sr" (Shiryaev–Roberts type, a sum of e-processes started at every time) or "cusum" (CUSUM type, a maximum). Both are e-detectors and both use the threshold arl, which for the CUSUM type is valid but conservative (Shin, Ramdas and Rinaldo, 2024, Section 2.5); "sr" is the default.
evalue	E-value family for the "bounded" class: "betting" (1 + lambda (x - center), tight for bounded data) or "hoeffding" (sub-Bernoulli exponential). Ignored by the other classes, which use their natural exponential e-values.
delta	Post-change shifts the mixture covers, in the units of the observations (positive numbers; the sign follows direction). Each shift is mapped to the bet lambda that is optimal for it in the class. The default is a geometric grid spanning small to large shifts.
weights	Mixture weights over delta, normalised internally. Default uniform.
phase1	Optional Phase I (in-control) data: a numeric vector for the "bounded" and "subgaussian" classes, or a data frame with columns x (counts) and n for "bernoulli" and "poisson". Used to set center (and sigma) when they are not declared; the source is recorded in the design and in every report.

Details

The guarantee is distribution-free within the class: for every pre-change distribution in it, the expected time to a false alarm is at least arl (Shin, Ramdas and Rinaldo, 2024, Theorem 2.4), and the probability of a false alarm by any time t, including data-dependent monitoring horizons, is at most t / arl (Ramdas, 2026). The price is paid in detection delay, which depends on the alternatives the mixture covers.

Value

An object of class edetect_design.

References

Shin, J., Ramdas, A. and Rinaldo, A. (2024). E-detectors: a nonparametric framework for sequential change detection. The New England Journal of Statistics in Data Science, 2(2), 229–260. doi:10.51387/23-NEJSDS51

Ramdas, A. (2026). Universality of e-detectors for ARL control. arXiv:2608.12660.

Examples

edetect_design(arl = 370, class = "bounded", center = 0.5, bounds = c(0, 1))
edetect_design(arl = 500, class = "bernoulli", center = 0.02, direction = "up")
edetect_design(arl = 370, class = "subgaussian", phase1 = rnorm(100), direction = "both")

---

Initialise an e-detector

Description

Initialise an e-detector

Usage

edetect_init(design)

Arguments

design

An edetect_design().

Value

An object of class edetect_chart holding the design, the running state and an empty trajectory.

Examples

design <- edetect_design(arl = 370, class = "bounded", center = 0.5, bounds = c(0, 1))
state <- edetect_init(design)
state

---

p chart: proportion of nonconforming units

Description

p chart: proportion of nonconforming units

Usage

edetect_p(x, n, center = NULL, phase1 = NULL, ...)

Arguments

x	Counts of nonconforming units per subgroup.
n	Subgroup sizes (one per subgroup or a single value).
center	Pre-change proportion; omit to estimate it from phase1.
phase1	Optional Phase I data frame with columns x and n.
...	Passed to edetect_design() (arl, direction, type, evalue, delta, weights).

Value

An edetect_chart.

Examples

chart <- edetect_p(x = c(1, 0, 2, 1, 3, 4, 5, 6), n = 100, center = 0.01, arl = 100)
edetect_alarm(chart)

---

Regression chart: monitoring residuals of a Phase I model

Description

Fits a linear model on Phase I data and monitors the Phase II residuals y - prediction as a sub-Gaussian stream centred at zero, with the residual standard deviation of the Phase I fit as the declared scale (or a sigma supplied by the user). The fitted model is kept in the chart.

Usage

edetect_regression(formula, phase1, phase2, sigma = NULL, ...)

Arguments

formula	Model formula.
phase1	Phase I data frame.
phase2	Phase II data frame with the same columns.
sigma	Declared sub-Gaussian scale of the residuals; default the Phase I residual standard deviation.
...	Passed to edetect_design() (arl, direction, type, evalue, delta, weights).

Value

An edetect_chart with an extra element fit.

Examples

set.seed(3)
d1 <- data.frame(z = 1:60); d1$y <- 2 + 0.5 * d1$z + rnorm(60, sd = 0.3)
d2 <- data.frame(z = 61:100)
d2$y <- 2 + 0.5 * d2$z + rnorm(40, sd = 0.3) + c(rep(0, 20), rep(1, 20))
chart <- edetect_regression(y ~ z, phase1 = d1, phase2 = d2, arl = 200)
edetect_alarm(chart)

---

The full report of a detector

Description

Everything a reader needs to audit an alarm or its absence: what was assumed (class, centre and its source, bounds or scale, direction), how the detector was built (type, e-value family, mixture), what was observed, the outcome and the software versions.

Usage

edetect_report(state)

Arguments

state

An edetect_chart.

Value

A list of class edetect_report.

Examples

design <- edetect_design(arl = 100, class = "bernoulli", center = 0.05)
state <- edetect_update(edetect_init(design), x = c(2, 3, 1, 4), n = 50)
edetect_report(state)

---

Restart a detector after an alarm

Description

Returns a fresh detector with the same design. The history of the previous run is kept in the runs element of the new object, so that a report can list every alarm.

Usage

edetect_restart(state)

Arguments

state

An edetect_chart that raised an alarm.

Value

A new edetect_chart.

Examples

design <- edetect_design(arl = 20, class = "subgaussian", center = 0, sigma = 1)
state <- suppressWarnings(edetect_update(edetect_init(design), c(rnorm(5), rnorm(30, 3))))
edetect_alarm(state)$alarm
state <- edetect_restart(state)
edetect_alarm(state)$alarm

---

u chart: nonconformities per unit of exposure

Description

u chart: nonconformities per unit of exposure

Usage

edetect_u(x, n, center = NULL, phase1 = NULL, ...)

Arguments

x	Counts per sample.
n	Exposure (area of opportunity) of each sample.
center	Pre-change rate per unit exposure; omit to estimate it from phase1.
phase1	Optional Phase I data frame with columns x and n.
...	Passed to edetect_design() (arl, direction, type, evalue, delta, weights).

Value

An edetect_chart.

Examples

chart <- edetect_u(x = c(3, 2, 4, 3, 8, 9, 11), n = c(2, 2, 2, 2, 2, 2, 2), center = 1.5, arl = 100)
edetect_alarm(chart)

---

Update an e-detector with new observations

Description

Feeds one or more Phase II observations, in time order, to the detector. The first time the statistic reaches the threshold an alarm is recorded; the detector does not accept further observations after that (see edetect_restart()).

Usage

edetect_update(state, x, n = NULL)

Arguments

state	An edetect_chart from edetect_init().
x	Numeric vector of observations (values for the "bounded" and "subgaussian" classes; counts for "bernoulli" and "poisson").
n	Subgroup sizes ("bernoulli") or exposures ("poisson"), one per observation or a single value. Ignored by the other classes.

Value

The updated edetect_chart.

Examples

design <- edetect_design(arl = 100, class = "subgaussian", center = 0, sigma = 1)
state <- edetect_init(design)
set.seed(1)
state <- edetect_update(state, c(rnorm(30), rnorm(30, mean = 1.5)))
edetect_alarm(state)

---

Individual-observation chart for bounded data

Description

Individual-observation chart for bounded data

Usage

edetect_x(x, bounds, center = NULL, phase1 = NULL, ...)

Arguments

x	Phase II observations.
bounds	Known bounds of the observations.
center	Pre-change mean; omit to estimate it from phase1.
phase1	Optional Phase I observations.
...	Passed to edetect_design() (arl, direction, type, evalue, delta, weights).

Value

An edetect_chart.

Examples

set.seed(2)
x <- c(runif(40, 0.3, 0.7), runif(40, 0.5, 0.9))
chart <- edetect_x(x, bounds = c(0, 1), center = 0.5, arl = 200)
edetect_alarm(chart)

---

Glance at a detector

Description

Glance at a detector

Usage

## S3 method for class 'edetect_chart'
glance(x, ...)

Arguments

x	An edetect_chart.
...	Unused.

Value

A one-row tibble: class, center, center_source, direction, type, arl, n_observed, alarm, alarm_time, evidence, change_estimate.

Examples

chart <- edetect_c(x = c(3, 2, 4, 3, 8, 9, 11), center = 3, arl = 100)
glance(chart)

---

Tidy the trajectory of a detector

Description

One row per observation with the mixed log e-value, the detector evidence (SR or CUSUM type, as designed), the CUSUM-type evidence, the threshold, the running change-point estimate and the alarm flag.

Usage

## S3 method for class 'edetect_chart'
tidy(x, ...)

Arguments

x	An edetect_chart.
...	Unused.

Value

A tibble with columns t, x, n, log_evalue, evidence, evidence_cusum, threshold, change_estimate, alarm.

Examples

chart <- edetect_c(x = c(3, 2, 4, 3, 8, 9, 11), center = 3, arl = 100)
tidy(chart)

---