p chart for the proportion of nonconforming items

Constructs a p chart from counts of nonconforming items in subgroups of size n. Subgroup sizes may vary; in that case, control limits are computed per observation.

Usage

shewhart_p(
  data,
  defects,
  n,
  index = NULL,
  limits = c("3sigma", "binomial"),
  rules = c("nelson_1_beyond_3s"),
  locale = getOption("shewhart.locale", "en"),
  verbose = NULL
)

Arguments

data

A data frame.

defects

Tidy-eval column reference for the count of nonconforming items in each subgroup.

n

Tidy-eval column reference for the subgroup size.

index

Optional tidy-eval column reference for the x-axis.

limits

One of "3sigma" (default; classical normal approximation) or "binomial" (exact 0.00135 / 0.99865 binomial quantiles, equivalent to the standard 3-sigma rate when n is large).

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_p.

Details

Standard 3-sigma limits use the normal approximation to the binomial: $$\bar p \pm 3 \sqrt{\bar p (1 - \bar p) / n_i}.$$ For very small n_i or very small / very large p_bar, the approximation deteriorates and exact binomial limits should be preferred (limits = "binomial").

References

Montgomery, D. C. (2019). Introduction to Statistical Quality Control (8th ed.). Wiley. Chapter 7.

Examples

set.seed(1)
df <- data.frame(
  day     = 1:30,
  defects = rbinom(30, size = 100, prob = 0.05),
  n       = 100
)
fit <- shewhart_p(df, defects = defects, n = n, index = day)
print(fit)
#> 
#> ── Shewhart chart p (proportion of nonconforming) ──────────────────────────────
#> • Observations / subgroups: 30
#> • Phase: "phase_1"
#> • Sigma estimate ("3sigma"): NA
#> 
#> ── Control limits ──
#> 
#> # A tibble: 3 × 4
#>   chart line   value note 
#>   <chr> <chr>  <dbl> <chr>
#> 1 p     CL    0.0517 ""   
#> 2 p     UCL   0.118  ""   
#> 3 p     LCL   0      ""   
#> ── Rule violations ──
#> 
#> ✔ No violations across 1 rule: "nelson_1_beyond_3s".