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.

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".