Acceptance Sampling Plans Design

Provides tools for designing and analyzing Acceptance Sampling plans. Supports both Attributes Sampling (Binomial and Poisson distributions) and Variables Sampling (Normal and Beta distributions), enabling quality control for fractional and compositional data. Uses nonlinear programming for sampling plan optimization, minimizing sample size while controlling producer's and consumer's risks. Operating Characteristic curves are available for plan visualization.

AccSamplingDesign

An R package for designing and analyzing acceptance sampling plans
📦 Now available on CRAN! 🎉 —

See NEWS.md for release notes and user-visible changes.

The package is described in Truong, Miranda, and Kissling (2026), AccSamplingDesign: An R Package for Optimizing Acceptance Sampling Plans, published in The R Journal.

Overview

The AccSamplingDesign package provides flexible tools to create and evaluate acceptance sampling plans in quality control, for both attributes (pass/fail) and variables (measurable) data. It supports optimization using nonlinear programming (NLP) to meet specified risks while minimizing the required sample size.

Key Features

• 🔍 Attribute Sampling (Binomial, Poisson): Decisions based on defect counts
• 📈 Variable Sampling (Normal, Beta): Including compositional data
• ⚙️ Risk-Based Optimization: Minimize sample size under alpha and beta constraints
• 📊 OC Curve Visualization: Plot Operating Characteristic curves
• 🔄 Custom Plan Comparison: Evaluate user-defined vs. optimized plans

Installation

# Install from CRAN
install.packages("AccSamplingDesign")

# Or install development version from GitHub
devtools::install_github("vietha/AccSamplingDesign")

# Load the package
library(AccSamplingDesign)

Examples

📌 Attribute Sampling (Binomial)

plan_attr <- optPlan(
  PRQ = 0.01,   # Acceptable quality
  CRQ = 0.05,   # Rejectable quality
  alpha = 0.02, # Producer's risk
  beta = 0.15,  # Consumer's risk
  distribution = "binomial"
)

summary(plan_attr)
accProb(plan_attr, 0.03)  # P(accept) if 3% defective
plot(plan_attr)           # OC curve

📌 Variable Sampling (Normal, Known Sigma)

plan_var <- optPlan(
  PRQ = 0.025,
  CRQ = 0.1,
  alpha = 0.05,
  beta = 0.10,
  distribution = "normal",
  sigma_type = "known"
)

summary(plan_var)
plot(plan_var)

📌 Variable Sampling (Normal, Unknown Sigma)

plan_var2 <- optPlan(
  PRQ = 0.025,
  CRQ = 0.1,
  alpha = 0.05,
  beta = 0.10,
  distribution = "normal",
  sigma_type = "unknown"
)

summary(plan_var2)

📌 Variable Sampling (Beta, Known Theta)

plan_beta <- optPlan(
  PRQ = 0.05,
  CRQ = 0.2,
  alpha = 0.05,
  beta = 0.10,
  distribution = "beta",
  theta = 44000000,
  theta_type = "known",
  LSL = 0.00001         # Lower Specification Limit
)

summary(plan_beta)
plot(plan_beta)              # By defect level
plot(plan_beta, by = "mean") # By mean value

📌 Variable Sampling (Beta, Unknown Theta)

Unknown-theta plans support analytical Delta--MLE ("delta_mle"), analytical Delta--MoM ("delta_mom"), and the earlier Govindaraju--Kissling sample-size adjustment ("gk_adjustment"). Delta--MLE is used when method is omitted.

plan_beta <- optPlan(
  PRQ = 0.05,
  CRQ = 0.2,
  alpha = 0.05,
  beta = 0.10,
  distribution = "beta",
  theta = 44000000,
  theta_type = "unknown",
  method = "delta_mle", # Default; may be omitted
  LSL = 0.00001
)

summary(plan_beta)
plot(plan_beta)              # By defect level
plot(plan_beta, by = "mean") # By mean value

📌 Compare Custom vs. Optimal Plans

pd <- seq(0, 0.15, by = 0.001)

oc_opt <- OCdata(plan = plan_attr, pd = pd)

mplan1 <- manualPlan(n = plan_attr$n, c = plan_attr$c - 1, distribution = "binomial")
oc_alt1 <- OCdata(plan = mplan1, pd = pd)

plot(pd, oc_opt$paccept, type = "l", col = "blue", lwd = 2,
     xlab = "Proportion Defective", ylab = "Probability of Acceptance",
     main = "OC Curves Comparison for Attributes Sampling Plan")
lines(pd, oc_alt1$paccept, col = "red", lwd = 2, lty = 2)
legend("topright", legend = c("Optimal Plan", "Manual Plan (c - 1)"),
       col = c("blue", "red"), lty = c(1, 2), lwd = 2)

Additional Notes

This README provides a quick start for using the AccSamplingDesign package. For a full discussion of the statistical foundations, models, and optimization methods used, please refer to the foundation sources such as:

• Schilling, E.G., & Neubauer, D.V. (2017). Acceptance Sampling in Quality Control (3rd ed.). CRC Press.
• Wilrich, P.T. (2004). In Frontiers in Statistical Quality Control 7.
• Govindaraju, K., & Kissling, R. (2015). Quality Engineering, 27(1), 1–13.

Contributing

Contributions, suggestions, and bug reports are welcome!
Please use GitHub Issues or submit a pull request.