Xbar-S control chart for rational subgroups

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

data

A data frame.

value

Tidy-eval column reference for the measurement.

subgroup

Tidy-eval column reference identifying the subgroup (e.g. shift, batch, hour). All subgroups must have equal size. Subgroups are plotted and tested in order of first appearance in data (time order), not in sorted order of their labels.

sigma_method

One of "sbar" (default; classical S-bar / c4(n)) or "pooled_sd" (pooled within-subgroup SD; preferred when subgroups have different sizes).

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_xbar_s.

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.

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)
#> 
#> ── Shewhart chart Xbar-S ───────────────────────────────────────────────────────
#> • Observations / subgroups: 30
#> • Phase: "phase_1"
#> • Sigma estimate ("sbar"): 0.5802
#> 
#> ── Control limits ──
#> 
#> # A tibble: 6 × 3
#>   chart line   value
#>   <chr> <chr>  <dbl>
#> 1 Xbar  CL    80.0  
#> 2 Xbar  UCL   80.5  
#> 3 Xbar  LCL   79.5  
#> 4 S     CL     0.567
#> 5 S     UCL    0.934
#> 6 S     LCL    0.201
#> ── Rule violations ──
#> 
#> ✔ No violations across 2 rules: "nelson_1_beyond_3s" and "nelson_2_nine_same".