Package {shewhartr}

shewhartr: Statistical Process Control with Tidyverse-Native Workflows

Description

The shewhartr package brings classical Statistical Process Control (SPC) methodology into a modern, tidy-friendly R workflow. It implements the full family of classical Shewhart control charts (I-MR, Xbar-R, Xbar-S, p, np, c, u), regression-based charts for processes with trend, runs tests (Nelson 1-8), Average Run Length (ARL) simulation, process capability indices, Box-Cox guidance, and an explicit Phase I / Phase II workflow.

Design principles

Tidyverse-native

All constructors take data as the first argument, support tidy evaluation for column references via {{ }}, and accept a .by argument where group-aware behaviour makes sense.

Object-oriented

Every chart returns an S3 object of class shewhart_chart (with a specific subclass like shewhart_i_mr) supporting print(), summary(), plot(), autoplot(), tidy(), glance() and augment().

Diagnostic-rich

Every chart can be passed through shewhart_runs() (configurable rule sets), shewhart_arl() (Monte Carlo ARL), shewhart_diagnostics() (Tukey-style residual panel) and shewhart_capability() (Cp, Cpk, Pp, Ppk with bootstrap CI).

Statistically honest

Counts are charted with exact Poisson limits when requested (limits = "poisson"), per Box's advice to model the right distribution rather than transform.

Robust alternatives

Most charts accept sigma_method = "biweight" for Tukey-style robust scale estimation as an alternative to the classical moving range.

Internationalisation

Plot labels and informative messages accept a locale argument ("en", "pt", "es", "fr").

The four families of functions

Classical charts (variables)

shewhart_i_mr(), shewhart_xbar_r(), shewhart_xbar_s().

Classical charts (attributes)

shewhart_p(), shewhart_np(), shewhart_c(), shewhart_u().

Regression-based chart

shewhart_regression() for trended processes, with optional automatic phase detection via the runs test.

Diagnostics & methodology

shewhart_runs(), shewhart_arl(), shewhart_diagnostics(), shewhart_box_cox(), shewhart_capability(), calibrate(), monitor().

Recommended starting points

New users should start with vignette("getting-started", package = "shewhartr") for a 5-minute overview, then move to the chart family that matches their data type. The vignette "phase1-phase2" explains the central distinction between estimation and monitoring, and "arl-simulation" shows how to evaluate the operating characteristics of any chart configuration.

Online documentation

The full reference manual, articles for every chart family, diagnostics and the case study are at https://castlaboratory.github.io/shewhartr/. Source, issues and contribution guide are at https://github.com/castlaboratory/shewhartr.

Author(s)

Maintainer: André Leite leite@castlab.org

Authors:

• André Leite leite@castlab.org

• Hugo Vasconcelos hugo.vasconcelos@ufpe.br

• Raydonal Ospina raydonal@castlab.org

• Cristiano Ferraz cferraz@castlab.org

Other contributors:

• Castlab [copyright holder, funder]

References

Shewhart, W. A. (1931). Economic Control of Quality of Manufactured Product. D. Van Nostrand.

Montgomery, D. C. (2019). Introduction to Statistical Quality Control (8th ed.). Wiley. ISBN: 978-1-119-39930-8.

Nelson, L. S. (1984). The Shewhart Control Chart - Tests for Special Causes. Journal of Quality Technology, 16(4), 237-239. doi:10.1080/00224065.1984.11978921

Woodall, W. H. (2000). Controversies and Contradictions in Statistical Process Control. Journal of Quality Technology, 32(4), 341-350. doi:10.1080/00224065.2000.11980013

Box, G. E. P., & Cox, D. R. (1964). An Analysis of Transformations. Journal of the Royal Statistical Society, Series B, 26(2), 211-252. doi:10.1111/j.2517-6161.1964.tb00553.x

Tukey, J. W. (1977). Exploratory Data Analysis. Addison-Wesley.

Wheeler, D. J., & Chambers, D. S. (1992). Understanding Statistical Process Control (2nd ed.). SPC Press.

See Also

Useful links:

• https://castlaboratory.github.io/shewhartr/

• https://github.com/castlaboratory/shewhartr

• Report bugs at https://github.com/castlaboratory/shewhartr/issues

Gompertz growth function

Description

Computes the value of the Gompertz curve parameterised in terms of starting value, asymptote, growth rate and lag:

G(x) = y_0 + (y_{\max} - y_0)\, \exp\!\left[-\exp\!\left(\frac{k\,e\,(\mathrm{lag} - x)}{y_{\max} - y_0} + 1\right)\right].

Usage

Gompertz(x, y0, ymax, k, lag)

Arguments

Details

This parameterisation, often called the "Zwietering Gompertz" form after Zwietering et al. (1990, eq. 3), gives directly interpretable parameters: y0 is the lower asymptote, ymax the upper asymptote, k the maximum growth rate (the slope of the curve at its inflection point), and lag the lag time (where the tangent at the inflection point crosses y0). The factor e is what makes k the maximum slope; versions of shewhartr up to 1.3.0 omitted it, so their curves had maximum slope k/e.

Value

A numeric vector the same length as x.

References

Gompertz, B. (1825). On the Nature of the Function Expressive of the Law of Human Mortality. Philosophical Transactions of the Royal Society of London, 115, 513-583.

Zwietering, M. H., Jongenburger, I., Rombouts, F. M., & van 't Riet, K. (1990). Modeling of the Bacterial Growth Curve. Applied and Environmental Microbiology, 56(6), 1875-1881. doi:10.1128/aem.56.6.1875-1881.1990

See Also

SSgompertzDummy() for an nls-friendly self-starting variant that allows a covariate shift.

Examples

x <- seq(0, 30, by = 0.5)
y <- Gompertz(x, y0 = 0, ymax = 100, k = 5, lag = 5)
plot(x, y, type = "l", main = "Gompertz growth curve")

Self-starting Gompertz with an additive dummy term

Description

Extends the classical Gompertz form by adding a linear contribution from a dummy covariate:

y = \mathrm{Asym}\,\exp(-b_2\,\exp(-b_3 x)) + \beta\,d.

Designed for use inside stats::nls(): starting values for the four parameters are computed automatically from the data, and the analytic gradient is supplied for faster, more reliable convergence.

Usage

SSgompertzDummy(x, dummy, Asym, b2, b3, Beta)

Arguments

Value

A numeric vector of fitted values, with attributes for self-starting and an analytic gradient.

References

Same as Gompertz().

See Also

stats::SSgompertz() for the standard self-starting Gompertz without a dummy term, fit_gompertz_dummy() for a convenience wrapper.

Examples

set.seed(42)
n <- 50
x <- seq(1, 10, length.out = n)
d <- rep(c(0, 1), each = n / 2)
y <- 100 * exp(-2 * exp(-0.3 * x)) + 20 * d + rnorm(n, 0, 3)
df <- data.frame(x = x, y = y, dummy = d)

fit <- nls(y ~ SSgompertzDummy(x, dummy, Asym, b2, b3, Beta), data = df)
summary(fit)

Convert a Shewhart chart to an interactive plotly figure

Description

Produces an interactive HTML plotly version of the chart that ggplot2::autoplot() would build for the same object. Useful for dashboards, reports, and any context where hovering, zooming and panning matters.

Usage

as_plotly(x, ...)

## Default S3 method:
as_plotly(x, ...)

## S3 method for class 'shewhart_chart'
as_plotly(
  x,
  tooltip = c("x", "y"),
  show_violations = TRUE,
  show_sigma_zones = FALSE,
  locale = NULL,
  ...
)

Arguments

Details

This is a separate function rather than an autoplot() argument so that loading shewhartr does not pull plotly (and its full transitive dependency tree) into every R session that uses the package. plotly lives in Suggests; install it explicitly if you want to use this function.

Value

A plotly object (S3 class plotly / htmlwidget) ready to print, embed in a Shiny app, or save with htmlwidgets::saveWidget().

Examples

if (requireNamespace("plotly", quietly = TRUE)) {
  set.seed(1)
  df  <- data.frame(t = 1:50, y = rnorm(50, mean = 100, sd = 2))
  fit <- shewhart_i_mr(df, value = y, index = t)
  as_plotly(fit)
}

Augment new data with control-chart annotations

Description

Returns the per-observation augmented tibble, optionally re-aligned against fresh data passed via newdata (Phase II monitoring). When newdata is NULL, returns the in-sample augmented tibble.

Usage

## S3 method for class 'shewhart_chart'
augment(x, newdata = NULL, ...)

Arguments

Value

A tibble. When newdata = NULL, the chart's augmented tibble; otherwise the same shape but for newdata.

Examples

set.seed(1)
df <- data.frame(y = rnorm(50))
fit <- shewhart_i_mr(df, value = y)
broom::augment(fit)

Plot a Shewhart chart with ggplot2

Description

Generic autoplot method that dispatches on chart subclass. All versions return a ggplot object that the user can further customise with the usual ggplot2 grammar.

Usage

autoplot.shewhart_chart(
  object,
  show_violations = TRUE,
  show_sigma_zones = FALSE,
  locale = NULL,
  ...
)

Arguments

Value

A ggplot object (or, for I-MR / Xbar-R / Xbar-S charts, a list of two ggplot objects with class shewhart_plot_pair that prints them stacked).

Examples

fit <- shewhart_i_mr(data.frame(y = rnorm(50)), value = y)
ggplot2::autoplot(fit)

Plot a regression control chart

Description

The autoplot() method for shewhart_regression() charts: per phase, a shaded band between dashed limits and a solid centre line; observations coloured by phase; out-of-control points ringed.

Usage

autoplot.shewhart_regression(
  object,
  show_violations = TRUE,
  show_sigma_zones = FALSE,
  locale = NULL,
  phase_dates = NULL,
  legend_position = c("top", "inside"),
  ...
)

Arguments

Value

A ggplot object.

Examples

pe <- subset(cvd_brazil, region == "PE" & date <= as.Date("2020-06-20"))
fit <- shewhart_regression(pe, value = new_deaths, index = date,
                           model = "log", limits_scale = "model",
                           phase_rule = "we_seven_same")
ggplot2::autoplot(fit, legend_position = "inside")
ggplot2::autoplot(fit, phase_dates = FALSE, locale = "pt")

Bacterial growth curve (optical density)

Description

A synthetic dataset of optical density (OD) measurements from a bacterial culture, sampled at 80 evenly spaced time points across a 24-hour incubation. The true mean follows a Gompertz growth curve with asymptote 1.2.

Usage

bacterial_growth

Format

A tibble with 80 rows and 2 columns:

hour

Numeric time in hours since inoculation.

od

Numeric optical density at 600 nm.

Source

Synthetic. See data-raw/build_all.R.

See Also

shewhart_regression() with model = "gompertz", Gompertz().

Examples

fit <- shewhart_regression(bacterial_growth,
                           value = od, index = hour,
                           model = "gompertz")
ggplot2::autoplot(fit)

Bottle filling volumes

Description

A synthetic dataset of 100 individual fill volumes (in millilitres). Process target is 500 ml with sigma 1.2 ml. A linear drift begins around observation 65, simulating a slowly miscalibrating filler.

Usage

bottle_fill

Format

A tibble with 100 rows and 2 columns:

observation

Integer observation index.

ml

Numeric volume in millilitres.

Source

Synthetic. See data-raw/build_all.R.

See Also

shewhart_i_mr().

Examples

fit <- shewhart_i_mr(bottle_fill, value = ml, index = observation)

ggplot2::autoplot(fit)

Apply / invert a Box-Cox power transformation

Description

The Box-Cox transformation (Box & Cox, 1964) is

y(\lambda) = \begin{cases} (x^\lambda - 1) / \lambda & \lambda \neq 0 \\ \log(x) & \lambda = 0. \end{cases}

Usage

box_cox(x, lambda)

Arguments

Details

For lambda = 0 this returns log(x); for lambda = 1 it returns x - 1 (no shape change). Use shewhart_box_cox() to estimate lambda from the data via profile log-likelihood.

Value

A numeric vector of transformed values.

References

Box, G. E. P., & Cox, D. R. (1964). An Analysis of Transformations. Journal of the Royal Statistical Society, Series B, 26(2), 211-252. doi:10.1111/j.2517-6161.1964.tb00553.x

See Also

shewhart_box_cox() to estimate lambda from data.

Examples

box_cox(1:10, lambda = 0)      # equivalent to log(1:10)
box_cox(1:10, lambda = 0.5)

Phase I calibration of a control chart

Description

Convenience wrapper that fits a control chart and tags its phase as "phase_1" (the default for any chart constructor). The intent is to make Phase I usage explicit in code: the practitioner acknowledges that limits are being estimated.

Usage

calibrate(data, ..., chart = "i_mr", trim_outliers = FALSE, max_trim_iter = 5L)

Arguments

Details

Optionally drops violations from the in-control estimate ("trimmed" calibration), per the iterative procedure described in Montgomery (2019) Section 6.2.3: if any observation falls outside the limits, it is removed and the limits are recomputed; iterate until either all remaining points are in control or no further trimming is possible.

Value

A shewhart_chart object with ⁠$phase = "phase_1"⁠.

References

Woodall, W. H. (2000). Controversies and Contradictions in Statistical Process Control. Journal of Quality Technology, 32(4), 341-350. doi:10.1080/00224065.2000.11980013

Montgomery, D. C. (2019). Introduction to Statistical Quality Control (8th ed.). Wiley. Section 6.2.3.

Examples

set.seed(1)
df <- data.frame(y = c(rnorm(40, mean = 100, sd = 2), 110, rnorm(20, 100, 2)))
calib <- calibrate(df, value = y, chart = "i_mr", trim_outliers = TRUE)
calib$n          # 60 if trim was avoided, fewer if outliers were removed

Daily insurance claim error rates

Description

A synthetic dataset of 30 days. Each day, a variable number of claims is processed (80-150) and the count of claims with errors is recorded. Underlying error rate is 5% for the first 22 days and 9% thereafter.

Usage

claims_p

Format

A tibble with 30 rows and 3 columns:

day

Integer day index (1-30).

n

Integer total claims processed that day.

defects

Integer claims found with errors.

Source

Synthetic. See data-raw/build_all.R.

See Also

shewhart_p().

Examples

fit <- shewhart_p(claims_p, defects = defects, n = n, index = day)

ggplot2::autoplot(fit)

Generate a qualitative HCL palette

Description

Internal palette used as a default when a number of phases or subgroups need distinct colours. For most plots, ggplot2's default palette is fine; this is provided for backward compatibility and quick prototyping.

Usage

color_hue(n)

Arguments

Value

A character vector of n hex colour strings.

Examples

color_hue(5)

COVID-19 daily mortality, Brazil, Pernambuco and Sao Paulo, 2020

Description

Daily count of new COVID-19 deaths officially recorded for Brazil as a whole, for the state of Pernambuco and for the state of Sao Paulo, from 25 February 2020 (Pernambuco: 12 March 2020, its first record) to 31 December 2020. These are the series analysed by Ferraz et al. (2020) with the regression chart on the log scale (shewhart_regression(model = "log", limits_scale = "model")).

Usage

cvd_brazil

Format

A tibble with 917 rows and 3 columns, in long format (one row per region and day, sorted by region then date):

date

Date of the bulletin.

region

Factor with levels "BR" (Brazil), "PE" (Pernambuco) and "SP" (Sao Paulo).

new_deaths

Integer count of new deaths reported that day.

Details

Values are kept exactly as published. The Pernambuco series has one negative value, new_deaths = -37 on 2020-09-03: a bulletin that revised the cumulative total downwards. Log-scale models reject it (log(1 + y) is undefined), so filter or reconcile it before fitting a chart that spans that date, e.g. subset(cvd_brazil, region == "PE" & new_deaths >= 0).

The articles used the Ministry of Health bulletins as available on 20 June 2020 (Revista Brasileira de Estatistica) and 24 July 2020 (SBPO). Later bulletins revised some days, so this snapshot can differ slightly from the data behind the published figures, and phase dates may move by a day or two.

Source

Wesley Cota, covid19br: number of confirmed cases and deaths by COVID-19 in Brazil (https://github.com/wcota/covid19br), compiled from the Brazilian Ministry of Health bulletins (https://covid.saude.gov.br). See data-raw/build_all.R.

References

Ferraz, C., Petenate, A. J., Leite Wanderley, A., Ospina, R., Torres, J., & Peruzzi Moreira, A. (2020). COVID-19: monitoramento por graficos de Shewhart. Revista Brasileira de Estatistica, 78(245), 23-41.

See Also

shewhart_regression(), cvd_recife.

Examples

table(cvd_brazil$region)

sp <- subset(cvd_brazil, region == "SP" & date >= as.Date("2020-03-17") &
               date <= as.Date("2020-06-20"))
fit <- shewhart_regression(sp, value = new_deaths, index = date,
                           model = "log", limits_scale = "model",
                           phase_rule = "we_seven_same")
ggplot2::autoplot(fit, legend_position = "inside")

COVID-19 daily mortality, Recife, Brazil, 2020

Description

Daily count of new COVID-19 deaths officially recorded in Recife (capital of Pernambuco state, Brazil) between 28 March 2020 and 31 December 2020. Distributed with v0.1.x as inst/extdata/recife_2020_covid19.rds and preserved in v1.0.0 as a vignette case study illustrating the regression-based control chart on non-stationary epidemiological counts.

Usage

cvd_recife

Format

A tibble with 279 rows and 3 columns:

date

Date of the bulletin.

new_deaths

Integer count of new deaths reported that day.

.t

Integer row index (1..N), useful as a continuous predictor for shewhart_regression().

Source

Castlab (Universidade Federal de Pernambuco) compiled the original series from the Brazilian Ministry of Health daily bulletins. See https://covid.saude.gov.br/.

See Also

shewhart_regression(), vignette("covid-recife", package = "shewhartr").

Examples

fit <- shewhart_regression(cvd_recife,
                           value = new_deaths, index = .t,
                           model = "loglog")
ggplot2::autoplot(fit)

Convenience wrapper to fit SSgompertzDummy to a data frame

Description

Convenience wrapper to fit SSgompertzDummy to a data frame

Usage

fit_gompertz_dummy(data, x, y, dummy, start = NULL, ...)

Arguments

Value

An object of class nls.

Examples

set.seed(42)
df <- data.frame(
  x = seq(1, 10, length.out = 50),
  d = rep(c(0, 1), each = 25)
)
df$y <- 100 * exp(-2 * exp(-0.3 * df$x)) + 20 * df$d + rnorm(50, 0, 3)
fit <- fit_gompertz_dummy(df, x = x, y = y, dummy = d)
coef(fit)

Glance at a Shewhart chart's overall diagnostics

Description

Returns a one-row tibble with overall chart-level diagnostics suitable for filling a row in a comparison table.

Usage

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

Arguments

Value

A one-row tibble with columns type, n, phase, sigma_hat, sigma_method, n_violations, n_rules, pct_violations. n_violations counts rule hits (one row per point and rule), while pct_violations is the share of points flagged by at least one rule, so it always lies in ⁠[0, 1]⁠.

Examples

fit <- shewhart_i_mr(data.frame(y = rnorm(50)), value = y)
broom::glance(fit)

Inverse log-log transformation

Description

Inverts loglog():

x = \alpha \,[\exp(\exp(y) - 1) - 1].

Usage

iloglog(x, alpha = 1)

Arguments

Value

A numeric vector on the original scale.

Examples

original <- c(0, 1, 5, 10, 100, 1000)
all.equal(original, iloglog(loglog(original)))

Inverse Box-Cox transformation

Description

Inverse Box-Cox transformation

Usage

inv_box_cox(x, lambda)

Arguments

Value

A numeric vector on the original scale.

Examples

y <- box_cox(1:10, lambda = 0.5)
inv_box_cox(y, lambda = 0.5)          # recovers 1:10
inv_box_cox(log(1:10), lambda = 0)    # lambda = 0 is exp()

Shewhart chart S3 class

Description

All chart constructors in the package return an object of class shewhart_chart with a more specific subclass (shewhart_i_mr, shewhart_xbar_r, shewhart_p, shewhart_regression, ...). The shared slots are type, augmented, limits, violations, fits, rules, sigma_hat, sigma_method, phase, n, call, and metadata. is_shewhart_chart() tests inheritance.

Usage

is_shewhart_chart(x)

Arguments

Value

Logical scalar.

Examples

fit <- shewhart_i_mr(data.frame(v = rnorm(30)), v)
is_shewhart_chart(fit)

Log-log transformation

Description

Applies the stabilising transformation

y = \log\!\bigl(\log\bigl(x/\alpha + 1\bigr) + 1\bigr).

Useful for very right-skewed non-negative data, particularly count processes with heavy tails. The +1 inside each log makes the transformation well-defined at zero.

Usage

loglog(x, alpha = 1)

Arguments

Value

A numeric vector of transformed values.

See Also

iloglog() for the inverse, shewhart_box_cox() for a data-driven transformation choice.

Examples

x <- c(0, 1, 5, 10, 100, 1000)
loglog(x)

Phase II monitoring against pre-calibrated limits

Description

Applies the control limits (and rule set) from a calibrated shewhart_chart object to fresh data. The new data must contain the same columns used by the original chart constructor.

Usage

monitor(data, chart)

Arguments

Details

Limits are not re-estimated; they are the limits stored on the calibration object. Only the violation table is recomputed against the new observations.

Value

A shewhart_chart object with ⁠$phase = "phase_2"⁠ and limits inherited from chart.

References

Woodall, W. H. (2000). Controversies and Contradictions in Statistical Process Control. Journal of Quality Technology, 32(4), 341-350.

Examples

set.seed(1)
base    <- data.frame(y = rnorm(50, mean = 100, sd = 2))
new_obs <- data.frame(y = rnorm(20, mean = 102, sd = 2))   # small shift
calib   <- calibrate(base, value = y, chart = "i_mr")
alarms  <- monitor(new_obs, calib)
alarms$violations

Solder defects on printed circuit boards

Description

A synthetic Poisson dataset: number of defective solder joints on each of 50 inspected printed circuit boards. The mean is 6, ideal for either the 3-sigma c chart or its more honest cousin with exact Poisson limits.

Usage

pcb_solder

Format

A tibble with 50 rows and 2 columns:

board

Integer board identifier.

defects

Integer count of defective joints.

Source

Synthetic. See data-raw/build_all.R.

See Also

shewhart_c().

Examples

fit       <- shewhart_c(pcb_solder, defects = defects, index = board)
fit_exact <- shewhart_c(pcb_solder, defects = defects, index = board,
                        limits = "poisson")

Print a Shewhart chart object

Description

Concise summary including chart type, sample size, sigma estimate and any rule violations. For full per-row results, use augment(); for a tabular limit summary, use tidy().

Usage

## S3 method for class 'shewhart_chart'
print(x, ...)

Arguments

Value

Returns x invisibly (for chaining).

Examples

set.seed(1)
fit <- shewhart_i_mr(data.frame(y = rnorm(50)), value = y)
print(fit)

Rolling sum with a configurable window

Description

Slides over x summing the last .window elements (including the current one). Treats NA as zero. Used internally by the runs tests.

Usage

rolling_sum(x, .window = 7L)

Arguments

Value

A numeric vector the same length as x.

Examples

rolling_sum(c(1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1), .window = 7)

Estimate Average Run Length via Monte Carlo simulation

Description

Simulates the run length of a Shewhart-type chart configuration under a sequence of mean shifts. For each shift size, replicates draw normal observations with mean shift * sigma (relative to the in-control centre) and stop at the first observation where any of the supplied rules fires. Returns a tibble with the average run length and a Monte Carlo confidence interval.

Usage

shewhart_arl(
  shift = seq(0, 3, by = 0.5),
  rules = c("nelson_1_beyond_3s", "nelson_2_nine_same"),
  n_sim = 5000L,
  max_run = 1000L,
  sigma = 1,
  seed = NULL
)

Arguments

Details

Computational note: for n_sim = 1e4 and a moderate set of rules, a single configuration takes a fraction of a second; a fine shift grid (10-15 points) takes a few seconds. For tighter intervals or larger rule sets, increase n_sim and/or set parallel = TRUE (currently a placeholder for future implementation).

Value

A tibble with columns shift, arl, arl_se, arl_lower, arl_upper, n_truncated. n_truncated counts how many replicates hit max_run before alarming (a sign that max_run should be raised).

References

Champ, C. W., & Woodall, W. H. (1987). Exact Results for Shewhart Control Charts with Supplementary Runs Rules. Technometrics, 29(4), 393-399. doi:10.1080/00401706.1987.10488262

Wald, A. (1947). Sequential Analysis. Wiley.

Examples

# In-control ARL of Nelson 1 (closed-form ARL_0 ~= 370.4)
set.seed(1)
shewhart_arl(shift = 0, rules = "nelson_1_beyond_3s",
             n_sim = 2000, max_run = 2000)

# Adding Nelson 2 sharpens detection but lowers ARL_0
shewhart_arl(shift = c(0, 0.5, 1, 1.5, 2),
             rules = c("nelson_1_beyond_3s", "nelson_2_nine_same"),
             n_sim = 2000)

Box-Cox profile log-likelihood

Description

Computes the profile log-likelihood for the Box-Cox power parameter lambda, applied to a single positive numeric series (regression to a constant) or to the residuals of a linear model.

Usage

shewhart_box_cox(data, value = NULL, lambda_grid = seq(-2, 2, by = 0.05))

Arguments

Details

Reports the lambda that maximises the profile likelihood and a 95% confidence interval based on the chi-square approximation to twice the log-likelihood drop (Box & Cox 1964, eq. 9).

Value

An object of class shewhart_box_cox with components profile (tibble of lambda vs. log-likelihood), lambda_hat (the maximiser), ci (95% CI). The object has its own print() method.

References

Box, G. E. P., & Cox, D. R. (1964). An Analysis of Transformations. Journal of the Royal Statistical Society, Series B, 26(2), 211-252. doi:10.1111/j.2517-6161.1964.tb00553.x

Examples

set.seed(1)
bc <- shewhart_box_cox(rlnorm(200, meanlog = 0, sdlog = 0.5))
bc$lambda_hat   # should be near 0 (log-normal data)

c chart for the number of nonconformities

Description

Constructs a c chart for counts of nonconformities (defects) per inspection unit, where the unit (area, length, time, etc.) is constant across observations. For variable inspection size use shewhart_u().

Usage

shewhart_c(
  data,
  defects,
  index = NULL,
  limits = c("3sigma", "poisson"),
  rules = c("nelson_1_beyond_3s"),
  locale = getOption("shewhart.locale", "en"),
  verbose = NULL
)

Arguments

Value

A shewhart_chart object of subclass shewhart_c.

References

Montgomery, D. C. (2019). Introduction to Statistical Quality Control (8th ed.). Wiley. Chapter 7.3.

Ryan, T. P. (2011). Statistical Methods for Quality Improvement (3rd ed.). Wiley. Chapter 6 (on the inadequacy of 3-sigma limits for low-mean Poisson counts).

Examples

set.seed(1)
df <- data.frame(
  unit    = 1:40,
  defects = rpois(40, lambda = 6)
)
fit <- shewhart_c(df, defects = defects, index = unit)
fit_exact <- shewhart_c(df, defects = defects, index = unit,
                        limits = "poisson")

Process capability indices Cp, Cpk, Pp, Ppk

Description

Computes the four classical capability indices for a Shewhart chart or a raw vector. Optionally returns bootstrap confidence intervals.

Usage

shewhart_capability(
  data,
  lsl = NA_real_,
  usl = NA_real_,
  target = NA_real_,
  ci_level = 0.95,
  n_boot = 2000L,
  seed = NULL
)

Arguments

Details

For a shewhart_chart of type i_mr, ewma, cusum, xbar_r or xbar_s, the within sigma stored on the chart object (sigma_hat, already expressed per individual measurement) is used for Cp/Cpk; the overall standard deviation of the individual measurements is used for Pp/Ppk. For subgroup charts the individual measurements are the ones the chart was built from (not the subgroup means). For a numeric vector data, a single sigma is used for both pairs (so Cp = Pp and Cpk = Ppk). Other chart types (attribute, regression, multivariate) are not supported; pass the measurements as a numeric vector instead.

Bootstrap intervals re-estimate sigma within in every replicate with the same estimator as the chart: whole subgroups are resampled for Xbar-R / Xbar-S charts, and consecutive pairs of observations (so that each replicate keeps its moving ranges) for individual charts.

Capability indices are only meaningful when the process is in statistical control (Phase I). The function emits a warning if the supplied chart has any rule violations.

Value

A list of class shewhart_capability with point estimates and (optionally) bootstrap CIs.

References

Kotz, S., & Lovelace, C. R. (1998). Process Capability Indices in Theory and Practice. Arnold.

Montgomery, D. C. (2019). Introduction to Statistical Quality Control (8th ed.). Wiley. Chapter 8.

Pearn, W. L., & Kotz, S. (2006). Encyclopedia and Handbook of Process Capability Indices. World Scientific.

Examples

set.seed(1)
df <- data.frame(y = rnorm(100, mean = 50, sd = 0.8))
fit <- shewhart_i_mr(df, value = y)
cap <- shewhart_capability(fit, lsl = 47, usl = 53, target = 50)
print(cap)

Look up Shewhart control chart constants

Description

Returns the classical Shewhart constants (A2, A3, c4, d2, d3, B3-B6, D3-D4) for a given subgroup size n. Tabulated values are used for n <= 25; for larger samples, c4 is computed from its closed form and the remaining constants are derived analytically when known (otherwise NA is returned with a warning).

Usage

shewhart_constants(n)

Arguments

Value

A data frame with columns n, A2, A3, c4, d2, d3, B3, B4, B5, B6, D3, D4.

References

Montgomery, D. C. (2019). Introduction to Statistical Quality Control (8th ed.). Wiley. Appendix VI.

Examples

shewhart_constants(5)
shewhart_constants(c(2, 5, 10, 25))

Tabular CUSUM control chart

Description

Constructs a two-sided tabular CUSUM chart for a single column of individual measurements. Two cumulative statistics, ⁠C+⁠ (upward) and ⁠C-⁠ (downward), are accumulated against a target with a reference value k; an alarm fires when either crosses the decision interval h * sigma.

Usage

shewhart_cusum(
  data,
  value,
  index = NULL,
  target = NULL,
  sigma = NULL,
  k = 0.5,
  h = 4,
  locale = getOption("shewhart.locale", "en"),
  verbose = NULL
)

Arguments

Details

By default, sigma is estimated from the moving range of value (MR_bar / 1.128); the target is the mean of value. Either can be overridden via target and sigma for Phase II monitoring against pre-calibrated values. Missing values in value are an error, since a single NA would propagate through the accumulators and silently disable every later alarm.

Value

A shewhart_chart object of subclass shewhart_cusum. The augmented slot has columns .value, .cusum_pos, .cusum_neg (the two accumulated statistics, both non-negative), .upper (the decision interval h * sigma), and .flag_signal.

References

Page, E. S. (1954). Continuous Inspection Schemes. Biometrika, 41(1-2), 100-115. doi:10.1093/biomet/41.1-2.100

Hawkins, D. M., & Olwell, D. H. (1998). Cumulative Sum Charts and Charting for Quality Improvement. Springer.

Montgomery, D. C. (2019). Introduction to Statistical Quality Control (8th ed.). Wiley. Chapter 9.

Examples

set.seed(1)
df <- data.frame(
  day = 1:80,
  y   = c(rnorm(40, mean = 100, sd = 2),
          rnorm(40, mean = 101, sd = 2))   # 0.5 sigma shift
)
fit <- shewhart_cusum(df, value = y, index = day)
print(fit)

ggplot2::autoplot(fit)

Tukey-style residual diagnostic panel

Description

For chart objects whose residuals are meaningful (shewhart_i_mr, shewhart_xbar_r, shewhart_xbar_s, shewhart_regression), produces the five-panel residual diagnostic favoured by exploratory data analysis: residuals vs. fitted, normal Q-Q, autocorrelation, moving-range plot of residuals, residual histogram. The aim is to make the assumptions that the chart is making visible: independence (ACF), normality (Q-Q, histogram), constant variance (residuals vs. fitted), and the absence of trend in dispersion (moving range).

Usage

shewhart_diagnostics(chart, locale = NULL)

Arguments

Value

A list of ggplot objects with class shewhart_diagnostics. The print method composes the panels.

References

Tukey, J. W. (1977). Exploratory Data Analysis. Addison-Wesley.

Box, G. E. P., Hunter, W. G., & Hunter, J. S. (2005). Statistics for Experimenters: Design, Innovation, and Discovery (2nd ed.). Wiley.

Examples

fit <- shewhart_i_mr(data.frame(y = rnorm(100)), value = y)
print(shewhart_diagnostics(fit))

Exponentially Weighted Moving Average (EWMA) control chart

Description

Constructs an EWMA chart for a single column of individual measurements. The chart is more sensitive than a Shewhart I chart to small but persistent shifts in the process mean, at the cost of a longer reaction time to large shifts.

Usage

shewhart_ewma(
  data,
  value,
  index = NULL,
  target = NULL,
  sigma = NULL,
  lambda = 0.2,
  L = 2.86,
  steady_state = FALSE,
  rules = "nelson_1_beyond_3s",
  locale = getOption("shewhart.locale", "en"),
  verbose = NULL
)

Arguments

Details

By default, sigma is estimated from the moving range of value (Wheeler 1992 convention, MR_bar / 1.128); the centre is the mean of value. Either can be overridden via target and sigma for Phase II monitoring against pre-calibrated values. Missing values in value are an error, since a single NA would propagate through the recursion and silently disable every later alarm.

Limits are time-varying by default: they widen out from target as the EWMA "warms up", converging to the asymptotic limits as i -> infinity. Set steady_state = TRUE to use the asymptotic limits everywhere (commonly chosen when calibrating from a long baseline).

Value

A shewhart_chart object of subclass shewhart_ewma. The augmented slot has columns .value (the original observation), .ewma (the smoothed statistic z_i, plotted on the chart), and the usual .center, .upper, .lower, ⁠.flag_*⁠.

References

Roberts, S. W. (1959). Control Chart Tests Based on Geometric Moving Averages. Technometrics, 1(3), 239-250. doi:10.1080/00401706.1959.10489860

Lucas, J. M., & Saccucci, M. S. (1990). Exponentially Weighted Moving Average Control Schemes: Properties and Enhancements. Technometrics, 32(1), 1-12. doi:10.1080/00401706.1990.10484583

Montgomery, D. C. (2019). Introduction to Statistical Quality Control (8th ed.). Wiley. Chapter 9.

Examples

set.seed(1)
df <- data.frame(
  day = 1:80,
  y   = c(rnorm(40, mean = 100, sd = 2),
          rnorm(40, mean = 101, sd = 2))   # 0.5 sigma shift
)
fit <- shewhart_ewma(df, value = y, index = day)
print(fit)

ggplot2::autoplot(fit)

Hotelling T-squared multivariate control chart

Description

Constructs a Hotelling ⁠T²⁠ chart for joint monitoring of p correlated quality characteristics. Use this chart when the variables genuinely co-vary — a classical example is a chemical process where temperature, pressure and flow rate are mechanically coupled, and a fault that breaks the coupling moves them off the joint distribution but possibly stays inside each marginal limit.

Usage

shewhart_hotelling(
  data,
  vars,
  subgroup = NULL,
  index = NULL,
  phase = c("phase_1", "phase_2"),
  alpha = 0.0027,
  locale = getOption("shewhart.locale", "en"),
  verbose = NULL
)

Arguments

Details

Both individual observations (subgroup = NULL) and rationally subgrouped observations (subgroup supplied) are supported. The chart selects the appropriate exact small-sample limits for the selected phase (Phase I uses retrospective limits derived from a Beta or F distribution; Phase II uses the slightly wider limits that propagate the Phase I parameter uncertainty to a fresh observation).

Value

A shewhart_chart object of subclass shewhart_hotelling. The augmented tibble has columns .t2 (the statistic), .upper (UCL — constant within a chart), .flag_signal and .flag_any, and one ⁠.contrib_<var>⁠ column per monitored variable giving that variable's marginal contribution to the alarm (Mason et al. 1995). The limits slot contains the chart-level UCL; the metadata slot stores the variable names, subgroup column name, and the parameters p, m, n, phase, alpha that determined the limit.

References

Hotelling, H. (1947). Multivariate quality control. In: Techniques of Statistical Analysis. McGraw-Hill.

Tracy, N. D., Young, J. C., & Mason, R. L. (1992). Multivariate control charts for individual observations. Journal of Quality Technology, 24(2), 88-95. doi:10.1080/00224065.1992.11979383

Mason, R. L., Tracy, N. D., & Young, J. C. (1995). Decomposition of ⁠T²⁠ for multivariate control chart interpretation. Journal of Quality Technology, 27(2), 99-108. doi:10.1080/00224065.1995.11979573

Mason, R. L., & Young, J. C. (2002). Multivariate Statistical Process Control with Industrial Applications. SIAM/ASA.

Montgomery, D. C. (2019). Introduction to Statistical Quality Control (8th ed.). Wiley. Chapter 11.

Examples

set.seed(1)
Sigma <- matrix(c(1, 0.7, 0.7, 1), 2, 2)
Z     <- MASS::mvrnorm(60, c(0, 0), Sigma)
df    <- tibble::tibble(t = 1:60, x1 = Z[, 1], x2 = Z[, 2])
fit   <- shewhart_hotelling(df, vars = c(x1, x2), index = t)
print(fit)

ggplot2::autoplot(fit)

Individuals and Moving Range (I-MR) control chart

Description

Constructs an I-MR chart for a single column of individual measurements. Returns a shewhart_chart object that supports print(), summary(), autoplot(), tidy(), glance() and augment().

Usage

shewhart_i_mr(
  data,
  value,
  index = NULL,
  sigma_method = c("mr", "median_mr", "biweight", "sd"),
  rules = c("nelson_1_beyond_3s", "nelson_2_nine_same"),
  locale = getOption("shewhart.locale", "en"),
  verbose = NULL
)

Arguments

Details

Sigma is estimated from the moving range with d2(2) = 1.128; the classical 3-sigma limits are equivalent to ⁠x_bar +/- 2.660 * MR_bar⁠. The MR chart limits are ⁠[0, D4(2) * MR_bar]⁠ with D4(2) = 3.267.

Value

A shewhart_chart object of subclass shewhart_i_mr.

References

Montgomery, D. C. (2019). Introduction to Statistical Quality Control (8th ed.). Wiley. Chapter 6.

Wheeler, D. J., & Chambers, D. S. (1992). Understanding Statistical Process Control (2nd ed.). SPC Press.

Examples

set.seed(1)
df <- data.frame(
  day = seq.Date(as.Date("2024-01-01"), by = "day", length.out = 60),
  y   = c(rnorm(40, mean = 100, sd = 2),
          rnorm(20, mean = 103, sd = 2))   # shift after position 40
)
fit <- shewhart_i_mr(df, value = y, index = day)
print(fit)

ggplot2::autoplot(fit)

Multivariate CUSUM control chart (Crosier 1988)

Description

Constructs a multivariate CUSUM chart for jointly monitoring p correlated variables. Like the univariate CUSUM it accumulates deviations from a target with a reference value k that decides when the accumulator resets; unlike a Hotelling T^2 chart it carries memory across observations and so detects small persistent shifts faster.

Usage

shewhart_mcusum(
  data,
  vars,
  index = NULL,
  target = NULL,
  cov = NULL,
  k = 0.5,
  h = NULL,
  locale = getOption("shewhart.locale", "en"),
  verbose = NULL
)

Arguments

Value

A shewhart_chart object of subclass shewhart_mcusum. The augmented tibble has columns .y (the chart statistic), .upper (the decision interval h), and .flag_signal.

References

Crosier, R. B. (1988). Multivariate Generalizations of Cumulative Sum Quality-Control Schemes. Technometrics, 30(3), 291-303. doi:10.1080/00401706.1988.10488402

Pignatiello, J. J., & Runger, G. C. (1990). Comparisons of Multivariate CUSUM Charts. Journal of Quality Technology, 22(3), 173-186. doi:10.1080/00224065.1990.11979237

Examples

set.seed(1)
Sigma <- matrix(c(1, 0.6, 0.6, 1), 2, 2)
base  <- MASS::mvrnorm(60, c(0, 0), Sigma)
shift <- MASS::mvrnorm(40, c(0.6, 0.6), Sigma)
df    <- data.frame(t = 1:100,
                    x1 = c(base[, 1], shift[, 1]),
                    x2 = c(base[, 2], shift[, 2]))
fit <- shewhart_mcusum(df, vars = c(x1, x2), index = t,
                       target = c(0, 0), cov = Sigma)
print(fit)

ggplot2::autoplot(fit)

Multivariate EWMA control chart

Description

Constructs a multivariate Exponentially Weighted Moving Average (MEWMA) chart for jointly monitoring p correlated variables. The chart is more sensitive than the Hotelling T^2 chart to small persistent shifts in the vector mean, in the same way the univariate EWMA is more sensitive than a Shewhart I chart.

Usage

shewhart_mewma(
  data,
  vars,
  index = NULL,
  target = NULL,
  cov = NULL,
  lambda = 0.1,
  h = NULL,
  steady_state = FALSE,
  locale = getOption("shewhart.locale", "en"),
  verbose = NULL
)

Arguments

Details

By default target (the in-control mean vector) and cov (the in-control covariance) are estimated from the data. For Phase II monitoring, supply both explicitly so the limits use the calibration values. The decision interval h is calibrated by lookup in a table giving ARL_0 ~ 200 (with known in-control parameters) for lambda in ⁠{0.05, 0.10, 0.20, 0.40}⁠ and ⁠p = 2..6⁠. There is one table for each covariance mode and the lookup follows steady_state; the steady-state table reproduces Prabhu & Runger (1997). If the ⁠(lambda, p)⁠ combination is outside the tabulated range, the user must pass h explicitly.

In Phase II (monitor()), the recursion continues from the last Phase I vector Z (and from the previous batch when monitor() is chained), with the covariance of the continued recursion.

Value

A shewhart_chart object of subclass shewhart_mewma. The augmented tibble has columns .t2 (the MEWMA statistic), .upper (the decision interval h), and .flag_signal.

References

Lowry, C. A., Woodall, W. H., Champ, C. W., & Rigdon, S. E. (1992). A Multivariate Exponentially Weighted Moving Average Control Chart. Technometrics, 34(1), 46-53. doi:10.1080/00401706.1992.10485232

Prabhu, S. S., & Runger, G. C. (1997). Designing a Multivariate EWMA Control Chart. Journal of Quality Technology, 29(1), 8-15. doi:10.1080/00224065.1997.11979721

Examples

set.seed(1)
Sigma <- matrix(c(1, 0.6, 0.6, 1), 2, 2)
base  <- MASS::mvrnorm(60, c(0, 0), Sigma)
shift <- MASS::mvrnorm(40, c(0.4, 0.4), Sigma)         # 0.4 sigma shift
df    <- data.frame(t = 1:100,
                    x1 = c(base[, 1], shift[, 1]),
                    x2 = c(base[, 2], shift[, 2]))
fit <- shewhart_mewma(df, vars = c(x1, x2), index = t,
                      target = c(0, 0), cov = Sigma,
                      lambda = 0.1)
print(fit)

ggplot2::autoplot(fit)

np chart for the number of nonconforming items

Description

Constructs an np chart from counts of nonconforming items in subgroups of constant size n. For variable subgroup sizes, use shewhart_p() instead.

Usage

shewhart_np(
  data,
  defects,
  n,
  index = NULL,
  rules = c("nelson_1_beyond_3s"),
  locale = getOption("shewhart.locale", "en"),
  verbose = NULL
)

Arguments

Value

A shewhart_chart object of subclass shewhart_np.

References

Montgomery, D. C. (2019). Introduction to Statistical Quality Control (8th ed.). Wiley. Chapter 7.2.2.

Examples

set.seed(1)
df <- data.frame(
  day     = 1:30,
  defects = rbinom(30, size = 200, prob = 0.04)
)
fit <- shewhart_np(df, defects = defects, n = 200, index = day)
print(fit)

p chart for the proportion of nonconforming items

Description

Constructs a p chart from counts of nonconforming items in subgroups of size n. Subgroup sizes may vary; in that case, control limits are computed per observation.

Usage

shewhart_p(
  data,
  defects,
  n,
  index = NULL,
  limits = c("3sigma", "binomial"),
  rules = c("nelson_1_beyond_3s"),
  locale = getOption("shewhart.locale", "en"),
  verbose = NULL
)

Arguments

Details

Standard 3-sigma limits use the normal approximation to the binomial:

\bar p \pm 3 \sqrt{\bar p (1 - \bar p) / n_i}.

For very small n_i or very small / very large p_bar, the approximation deteriorates and exact binomial limits should be preferred (limits = "binomial").

Value

A shewhart_chart object of subclass shewhart_p.

References

Montgomery, D. C. (2019). Introduction to Statistical Quality Control (8th ed.). Wiley. Chapter 7.

Examples

set.seed(1)
df <- data.frame(
  day     = 1:30,
  defects = rbinom(30, size = 100, prob = 0.05),
  n       = 100
)
fit <- shewhart_p(df, defects = defects, n = n, index = day)
print(fit)

Access the package's named colour palettes

Description

Returns one of the curated colour vectors that every chart in the package draws from. Useful when extending an autoplot() chart with your own layers and you want them to match the rest of the package's visual identity.

Usage

shewhart_palette(
  name = c("phase_seq", "family", "signal", "neutral"),
  n = NULL
)

Arguments

Details

phase_seq

Sequential palette for time-ordered phase indices in regression / multi-phase charts. Cool blues at the baseline, warming through neutral to terracotta as phase index grows. Avoids saturated red (reserved for signal).

family

Named categorical palette for the four chart families: variables, attributes, memory-based, multivariate. Identical to the colours used in the architecture diagram.

signal

Two-colour palette: in_control (deep blue) and out_of_control (firebrick). Used to colour violation points on every chart so the alarm signal is consistent.

neutral

Structural greys used by shewhart_theme() for backgrounds, gridlines and text colour.

Value

A character vector of colour hex codes; for family and signal, the vector is named.

Examples

shewhart_palette("phase_seq", n = 4)
shewhart_palette("family")["multivariate"]
shewhart_palette("signal")

Regression-based control chart for processes with trend

Description

Fits a chosen model to the data (linear, log, log-log, Gompertz, logistic, or a user-supplied formula), then constructs control limits around the fitted curve using the moving-range estimator on the residuals (Wheeler 1992). Optionally detects phase changes automatically via runs tests on the residuals and re-fits each phase.

Usage

shewhart_regression(
  data,
  value,
  index,
  model = c("auto", "linear", "log", "loglog", "gompertz", "logistic"),
  formula = NULL,
  dummy = NULL,
  start_base = NULL,
  phase_changes = NULL,
  phase_rule = "nelson_2_nine_same",
  rules = c("nelson_1_beyond_3s", "nelson_2_nine_same"),
  sigma_method = c("mr", "median_mr", "biweight", "sd"),
  lower_bound = NA_real_,
  limits_scale = c("original", "model"),
  locale = getOption("shewhart.locale", "en"),
  verbose = NULL
)

Arguments

Details

This is the package's flagship chart, intended for trended or non-stationary processes for which classical Shewhart charts give systematically wrong limits. See the vignette regression-charts for a thorough discussion and examples.

Models that take the logarithm of the response ("log", "loglog", and "auto" whenever it selects "log") require non-negative values: log(1 + y) is undefined for a negative count such as a bulletin that revises a cumulative total downwards. The function stops with an error naming the offending row instead of returning NaN limits; filter or reconcile such rows first.

A Phase I chart refits every phase, including the last one (labelled "Monitoring"). To judge new observations against the limits of the last phase projected forward, as in a prospective analysis, calibrate on the data up to the end of the last phase with calibrate() and pass the rest to monitor(): it continues .N, uses the stored sigma, and honours limits_scale and lower_bound. A prospective replay in the manner of Ferraz et al. (2020) chains these steps one phase at a time: calibrate a single phase (phase_changes = integer(0)) on its first observations, monitor the rows that follow, and start the next phase at the first index after the first run flagged by "we_seven_same" (column .flag_we_seven_same of the monitored chart, with rules = "we_seven_same").

Value

A shewhart_chart object of subclass shewhart_regression. The fits slot contains a list of fitted model objects (one per phase; a phase with fewer than 3 observations reuses the previous phase's fit). The metadata slot additionally stores phase_n_end (the last within-phase position .N reached by each phase's fit) and phase_sigma (the residual sigma of each phase), which monitor() uses to extrapolate the last phase, together with limits_scale and lower_bound. The sigma_hat slot is the median of the per-phase sigmas.

The .phase_label column names the phases "Base", "Phase 1", ..., "Monitoring" (localised). When the index column is a Date (or a date-time), every phase but the last also carries its end date, e.g. "Base (until 2020-05-11)". The first index value of each phase is the date on which it starts.

References

Mandel, B. J. (1969). The Regression Control Chart. Journal of Quality Technology, 1(1), 1-9. doi:10.1080/00224065.1969.11980341

Wheeler, D. J., & Chambers, D. S. (1992). Understanding Statistical Process Control (2nd ed.). SPC Press.

Perla, R. J., Provost, S. M., Parry, G. J., Little, K., & Provost, L. P. (2020). Understanding variation in reported COVID-19 deaths with a novel Shewhart chart application. International Journal for Quality in Health Care, 32(10), 685-688. doi:10.1093/intqhc/mzaa069

Ferraz, C., Petenate, A. J., Leite Wanderley, A., Ospina, R., Torres, J., & Peruzzi Moreira, A. (2020). COVID-19: monitoramento por graficos de Shewhart. Revista Brasileira de Estatistica, 78(245), 23-41.

Box, G. E. P., & Cox, D. R. (1964). An Analysis of Transformations. Journal of the Royal Statistical Society, Series B, 26(2), 211-252. doi:10.1111/j.2517-6161.1964.tb00553.x

Examples

set.seed(1)
df <- data.frame(
  t = 1:60,
  y = c(1:30 * 0.5 + rnorm(30, sd = 0.5),    # phase 1: linear trend
        15 + 1:30 * 0.1 + rnorm(30, sd = 0.5)) # phase 2: shift + slowdown
)
fit <- shewhart_regression(df, value = y, index = t, model = "linear")
print(fit)
ggplot2::autoplot(fit)

# Multiplicative limits built on the log scale (Perla et al. 2020;
# Ferraz et al. 2020): base of 10 days, 7-point shift rule
br <- subset(cvd_brazil, region == "BR" & date >= as.Date("2020-03-17") &
               date <= as.Date("2020-06-20"))
fit_log <- shewhart_regression(br, value = new_deaths, index = date,
                               model = "log", limits_scale = "model",
                               phase_rule = "we_seven_same")
ggplot2::autoplot(fit_log, legend_position = "inside")

List available runs rules

Description

List available runs rules

Usage

shewhart_rules_available()

Value

A tibble with columns rule (the key) and description.

Examples

shewhart_rules_available()

Apply runs tests to a chart object or to raw vectors

Description

Implements the eight rules of Nelson (1984, 1985) plus a Western Electric "7 in a row" variant for backward compatibility. Returns a tidy tibble of rule violations.

Usage

shewhart_runs(
  x,
  rules = c("nelson_1_beyond_3s", "nelson_2_nine_same"),
  center = NULL,
  sigma = NULL
)

Arguments

Value

A tibble with columns position (integer, the index where the rule fired), rule (character key), description (character label), value (the value at that position) and severity (currently always "out_of_control"; reserved for future warning-level rules).

References

Nelson, L. S. (1984). The Shewhart Control Chart – Tests for Special Causes. Journal of Quality Technology, 16(4), 237-239. doi:10.1080/00224065.1984.11978921

Nelson, L. S. (1985). Interpreting Shewhart Xbar Control Charts. Journal of Quality Technology, 17(2), 114-117. doi:10.1080/00224065.1985.11978941

Western Electric Co. (1956). Statistical Quality Control Handbook.

Examples

set.seed(1)
x <- c(rnorm(20), 5, rnorm(20))    # one outlier at position 21
shewhart_runs(x, center = 0, sigma = 1)

Editorial-style ggplot2 theme used by every ⁠autoplot.shewhart_*⁠

Description

Shared across the package so charts look like one family. The visual choices are inspired by data-journalism graphics (FT, Pew Research, The Economist): off-white background, only horizontal grid lines, axis line on the data side, left-aligned title block, and tonal grey for non-data ink.

Usage

shewhart_theme(base_size = 10.5, base_family = "")

Arguments

Details

Use it from your own layers when you want a chart that matches the package's identity:

ggplot(d, aes(x, y)) + geom_line() + shewhart_theme()

Value

A ggplot2::theme() object.

Examples

library(ggplot2)
df <- data.frame(x = 1:50, y = cumsum(rnorm(50)))
ggplot(df, aes(x, y)) + geom_line() + shewhart_theme()

u chart for nonconformities per unit, variable inspection size

Description

Constructs a u chart from defect counts and a per-observation "exposure" (inspection size: square metres of fabric, hours of operation, lines of code, etc.). For constant exposure use shewhart_c().

Usage

shewhart_u(
  data,
  defects,
  exposure,
  index = NULL,
  limits = c("3sigma", "poisson"),
  rules = c("nelson_1_beyond_3s"),
  locale = getOption("shewhart.locale", "en"),
  verbose = NULL
)

Arguments

Value

A shewhart_chart object of subclass shewhart_u.

References

Montgomery, D. C. (2019). Introduction to Statistical Quality Control (8th ed.). Wiley. Chapter 7.3.2.

Examples

set.seed(1)
df <- data.frame(
  roll     = 1:25,
  defects  = rpois(25, lambda = 4 * runif(25, 0.5, 1.5)),
  m2       = runif(25, 0.5, 1.5)    # variable inspection size
)
fit <- shewhart_u(df, defects = defects, exposure = m2, index = roll)

Xbar-R control chart for rational subgroups

Description

Constructs a paired Xbar (subgroup mean) and R (subgroup range) chart for measurements organised in rational subgroups of size 2 to 10. Sigma is estimated from the average within-subgroup range.

Usage

shewhart_xbar_r(
  data,
  value,
  subgroup,
  rules = c("nelson_1_beyond_3s", "nelson_2_nine_same"),
  locale = getOption("shewhart.locale", "en"),
  verbose = NULL
)

Arguments

Details

Xbar-chart limits use A2(n); R-chart limits use D3(n) and D4(n). See shewhart_constants() for the tabulated values.

Value

A shewhart_chart object of subclass shewhart_xbar_r.

References

Montgomery, D. C. (2019). Introduction to Statistical Quality Control (8th ed.). Wiley. Chapter 6.

Shewhart, W. A. (1931). Economic Control of Quality of Manufactured Product. D. Van Nostrand.

Examples

set.seed(1)
df <- data.frame(
  batch = rep(1:25, each = 5),
  y     = rnorm(125, mean = 50, sd = 1.5)
)
fit <- shewhart_xbar_r(df, value = y, subgroup = batch)
print(fit)

Xbar-S control chart for rational subgroups

Description

Like shewhart_xbar_r(), but uses the subgroup standard deviation (S) instead of the range. Recommended for subgroup sizes greater than 10, or when subgroup sizes differ.

Usage

shewhart_xbar_s(
  data,
  value,
  subgroup,
  sigma_method = c("sbar", "pooled_sd"),
  rules = c("nelson_1_beyond_3s", "nelson_2_nine_same"),
  locale = getOption("shewhart.locale", "en"),
  verbose = NULL
)

Arguments

Details

Xbar-chart limits use A3(n); S-chart limits use B3(n) and B4(n). When sigma_method = "pooled_sd", sigma is estimated as the pooled within-subgroup standard deviation.

Value

A shewhart_chart object of subclass shewhart_xbar_s.

References

Montgomery, D. C. (2019). Introduction to Statistical Quality Control (8th ed.). Wiley. Chapter 6.4.

Examples

set.seed(1)
df <- data.frame(
  batch = rep(1:30, each = 12),
  y     = rnorm(360, mean = 80, sd = 0.6)
)
fit <- shewhart_xbar_s(df, value = y, subgroup = batch)
print(fit)

Compact tibble-like summary

Description

Compact tibble-like summary

Usage

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

Arguments

Value

A list with elements limits and violations.

Examples

fit <- shewhart_i_mr(data.frame(y = rnorm(50)), value = y)
summary(fit)

Pharmaceutical tablet weights

Description

A synthetic dataset modelled on classical pharmaceutical quality control. Tablet weights are recorded in subgroups of 5 tablets each, across 25 production batches. Target weight is 250 mg with a process sigma of 1.5 mg; a small mean shift to 251.5 mg is embedded in subgroups 18-25.

Usage

tablet_weight

Format

A tibble with 125 rows and 3 columns:

subgroup

Integer batch identifier (1-25).

tablet

Integer tablet position within the batch (1-5).

weight

Numeric tablet weight in milligrams.

Source

Synthetic. See data-raw/build_all.R.

See Also

shewhart_xbar_r(), shewhart_xbar_s().

Examples

fit <- shewhart_xbar_r(tablet_weight, value = weight, subgroup = subgroup)

ggplot2::autoplot(fit)

Curing oven temperature drift

Description

A synthetic dataset of 200 sensor readings on a curing oven. The true temperature exhibits a slow linear drift superimposed on a periodic component. A classical Shewhart chart will misjudge the limits because the process is non-stationary - a regression control chart is the right tool.

Usage

temperature_drift

Format

A tibble with 200 rows and 2 columns:

minute

Integer minute since start.

temp_c

Numeric temperature in degrees Celsius.

Source

Synthetic. See data-raw/build_all.R.

See Also

shewhart_regression().

Examples

fit <- shewhart_regression(temperature_drift,
                           value = temp_c, index = minute,
                           model = "linear")
ggplot2::autoplot(fit)

Tidy the control limits of a Shewhart chart

Description

Returns a tibble of the chart's control limits in tall format. Each row corresponds to one line of one chart panel (CL / UCL / LCL).

Usage

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

Arguments

Value

A tibble with at least columns chart, line, value. For regression charts, whose limits follow a fitted curve, the tibble is in long format with one row per phase, endpoint and line: columns chart ("regression"), .phase, endpoint ("first" / "last" observation of the phase), line ("CL", "UCL", "LCL") and value.

Examples

fit <- shewhart_i_mr(data.frame(y = rnorm(50)), value = y)
broom::tidy(fit)