Individuals and Moving Range (I-MR) control chart

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

data

A data frame.

value

Tidy-eval column reference for the measurement.

index

Optional tidy-eval column reference for the x-axis (date or integer). If NULL (default), the row index is used.

sigma_method

One of "mr" (default; classical moving range), "median_mr" (Tukey-style robust: median of moving ranges, with bias correction), "biweight" (Tukey biweight midvariance), "sd" (sample SD).

rules

Character vector of rule keys to apply. See shewhart_rules_available(). Default applies Nelson 1 and 2.

locale

One of "en", "pt", "es", "fr". Affects plot labels and informative messages.

verbose

Logical. Print progress messages? Defaults to the shewhart.verbose option.

Value

A shewhart_chart object of subclass shewhart_i_mr.

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.

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)
#> 
#> ── Shewhart chart I-MR (individuals & moving range) ────────────────────────────
#> • Observations / subgroups: 60
#> • Phase: "phase_1"
#> • Sigma estimate ("mr"): 1.704
#> 
#> ── Control limits ──
#> 
#> # A tibble: 6 × 3
#>   chart line   value
#>   <chr> <chr>  <dbl>
#> 1 I     CL    101.  
#> 2 I     UCL   106.  
#> 3 I     LCL    96.1 
#> 4 MR    CL      1.92
#> 5 MR    UCL     6.28
#> 6 MR    LCL     0   
#> ── Rule violations ──
#> 
#> ! 10 violations across 2 rules.
#> nelson_1_beyond_3s: 3 hits.
#> nelson_2_nine_same: 7 hits.
# \donttest{
ggplot2::autoplot(fit)
#> Warning: Removed 1 row containing missing values or values outside the scale range
#> (`geom_line()`).
#> Warning: Removed 1 row containing missing values or values outside the scale range
#> (`geom_point()`).

# }