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Process capability indices Cp, Cpk, Pp, Ppk

Source: R/capability.R
shewhart_capability.Rd

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, ewma, cusum, xbar_r or xbar_s, the within sigma stored on the chart object (sigma_hat, already expressed per individual measurement) is used for Cp/Cpk; the overall standard deviation of the individual measurements is used for Pp/Ppk. For subgroup charts the individual measurements are the ones the chart was built from (not the subgroup means). For a numeric vector data, a single sigma is used for both pairs (so Cp = Pp and Cpk = Ppk). Other chart types (attribute, regression, multivariate) are not supported; pass the measurements as a numeric vector instead.

Bootstrap intervals re-estimate sigma within in every replicate with the same estimator as the chart: whole subgroups are resampled for Xbar-R / Xbar-S charts, and consecutive pairs of observations (so that each replicate keeps its moving ranges) for individual charts.

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  1.19  1.59
#> 2 Cpk    1.33  1.14  1.55
#> 3 Pp     1.39  1.23  1.63
#> 4 Ppk    1.35  1.18  1.58
# }