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Calculate Control Limits

Source: R/control-limits.R
measure_control_limits.Rd

Calculates control limits for quality control monitoring using Shewhart rules and optionally EWMA or CUSUM statistics.

Usage

measure_control_limits(
  data,
  response_col,
  group_col = NULL,
  type = c("shewhart", "ewma", "cusum"),
  n_sigma = 3,
  target = NULL,
  lambda = 0.2,
  k = 0.5,
  h = 5
)

Arguments

data

A data frame containing QC measurements.

response_col

Name of the column containing QC values.

group_col

Optional grouping column (e.g., for different QC levels).

type

Type of control chart: "shewhart" (default), "ewma", or "cusum".

n_sigma

Number of standard deviations for control limits. Default is 3.

target

Optional target value. If NULL, calculated from data mean.

lambda

EWMA smoothing parameter (0 < lambda <= 1). Default is 0.2.

k

CUSUM slack parameter. Default is 0.5 (in sigma units).

h

CUSUM decision interval. Default is 5 (in sigma units).

Value

A measure_control_limits object containing:

  • center: Center line (target or mean)

  • lcl: Lower control limit

  • ucl: Upper control limit

  • lwl: Lower warning limit (2 sigma)

  • uwl: Upper warning limit (2 sigma)

  • sigma: Estimated standard deviation

  • Additional statistics depending on chart type

Details

Shewhart Charts

Classic control charts with limits at mean +/- n*sigma:

  • UCL/LCL: Action limits (typically 3 sigma)

  • UWL/LWL: Warning limits (typically 2 sigma)

EWMA Charts

Exponentially weighted moving average, more sensitive to small shifts:

  • Control limits narrow as more data is collected

  • Lambda parameter controls weight of recent observations

CUSUM Charts

Cumulative sum chart for detecting persistent shifts:

  • Upper and lower CUSUM statistics track cumulative deviations

  • Decision interval h determines sensitivity

See also

measure_control_chart(), measure_system_suitability()

Other control-charts: measure_control_chart(), measure_system_suitability()

Examples

# Calculate Shewhart control limits
set.seed(123)
qc_data <- data.frame(
  run_order = 1:30,
  qc_value = rnorm(30, mean = 100, sd = 2)
)
limits <- measure_control_limits(qc_data, "qc_value")
print(limits)
#> measure_control_limits: shewhart chart
#> ──────────────────────────────────────────────────────────────────────────────── 
#> 
#>   n = 30 
#>   Center = 99.91 
#>   Sigma = 1.962 
#>   UCL (+3s) = 105.8 
#>   UWL (+2s) = 103.8 
#>   LWL (-2s) = 95.98 
#>   LCL (-3s) = 94.02 
#> 

# EWMA control limits
limits_ewma <- measure_control_limits(qc_data, "qc_value", type = "ewma")