Regression-based control chart for processes with trend — shewhart

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 = 10L,
  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_,
  locale = getOption("shewhart.locale", "en"),
  verbose = NULL
)

Arguments

data: A data frame.
value: Tidy-eval column reference for the response.
index: Tidy-eval column reference for the predictor (typically time, but can be any continuous variable).
model: Character. One of "auto" (Box-Cox guidance), "linear", "log" (fits log(y + 1) ~ N), "loglog", "gompertz", "logistic". For full control, supply formula instead.
formula: Optional one-sided or two-sided formula referencing columns in data. If provided, overrides model.
dummy: Optional tidy-eval column reference for an additive covariate (a "dummy" in the original v0.1 nomenclature; can be any factor or numeric covariate the user wants to adjust for, such as day-of-week effects or treatment indicators).
start_base: Integer. Number of initial observations used to estimate the first phase. Defaults to 10.
phase_changes: Optional vector of index positions or values at which to force a phase change. If NULL, phase changes are detected automatically using the supplied phase_rule.
phase_rule: Character. Runs rule used to detect new phases. See shewhart_rules_available(). Default Nelson 2 (9 points same side; ARL_0 ~ 256). For backward compatibility with v0.1.x, use "we_seven_same" (7 points; ARL_0 ~ 64).
rules: Character vector of rules to flag on the final chart.
sigma_method: One of "mr" (default), "median_mr", "biweight" (Tukey-style robust), or "sd".
lower_bound: Numeric scalar or NA. If non-NA, lower limit is clipped at this value (commonly 0 for counts). Default NA (no clipping).
locale: Character. One of "en", "pt", "es", "fr".
verbose: Logical. Print progress messages?

Value

A shewhart_chart object of subclass shewhart_regression. The fits slot contains a list of fitted model objects (one per phase).

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.

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.

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

# \donttest{
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)
#> 
#> ── Shewhart chart regression-based ─────────────────────────────────────────────
#> • Observations / subgroups: 60
#> • Phase: "phase_1"
#> • Sigma estimate ("mr"): 0.4273
#> 
#> ── Control limits ──
#> 
#> # A tibble: 4 × 7
#>   .phase cl_first ucl_first lcl_first cl_last ucl_last lcl_last
#>    <int>    <dbl>     <dbl>     <dbl>   <dbl>    <dbl>    <dbl>
#> 1      0    0.443      1.82    -0.936    5.19     6.57     3.81
#> 2      1    5.52       6.96     4.07    10.2     11.7      8.79
#> 3      2   11.2       12.5      9.96    16.3     17.6     15.0 
#> 4      3   15.9       17.2     14.7     18.1     19.3     16.8 
#> ── Rule violations ──
#> 
#> ! 1 violation across 2 rules.
#> nelson_1_beyond_3s: 1 hit.
ggplot2::autoplot(fit)

# }