Process capability indices Cp, Cpk, Pp, Ppk — shewhart

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

data: A shewhart_chart object or a numeric vector.
lsl, usl: Numeric scalars. Lower and upper specification limits. At least one must be supplied.
target: Numeric scalar. Optional process target. If missing, defaults to the midpoint of (lsl, usl).
ci_level: Numeric. Confidence level for bootstrap intervals. Default 0.95. Set to NA to skip bootstrap.
n_boot: Integer. Number of bootstrap replicates. Default 2000.
seed: Optional integer for reproducibility.

Value

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

Details

For a shewhart_chart of type i_mr, xbar_r, or xbar_s, the within-subgroup sigma stored on the chart object is used for Cp/Cpk; the overall standard deviation of the raw data is used for Pp/Ppk. For a numeric vector data, a single sigma is used for both pairs (so Cp = Pp and Cpk = Ppk).

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.

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

# \donttest{
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)
#> 
#> ── Process capability ──────────────────────────────────────────────────────────
#> • n = 100, mean = 50.0871
#> • Sigma within = 0.73, sigma overall = 0.7186
#> • LSL = 47, USL = 53, target = 50
#> 
#> ── Indices ──
#> 
#> # A tibble: 4 × 4
#>   index value lower upper
#>   <chr> <dbl> <dbl> <dbl>
#> 1 Cp     1.37  1.23  1.63
#> 2 Cpk    1.33  1.18  1.58
#> 3 Pp     1.39  1.23  1.63
#> 4 Ppk    1.35  1.18  1.58
# }