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AccSamplingDesign: Acceptance Sampling Plan Design - R Package

Ha Truong

2025-07-19

Introduction

The AccSamplingDesign package provides tools to create and evaluate acceptance sampling plans for both attribute and variable quality data. The focus is on controlling producer’s and consumer’s risk specifications while minimizing required sample sizes.

The package supports:

Attribute sampling plans (e.g., pass/fail outcomes)
Variable sampling plans under Normal and Beta distributions
Easy-to-use functions for computing acceptance probability and visualizing OC curves

Installation

Install from CRAN:

install.packages("AccSamplingDesign")

Or from GitHub:

devtools::install_github("vietha/AccSamplingDesign")

Attributes Sampling Example

# Create an attribute plan with binomial assumption
plan_attr <- optPlan(
  PRQ = 0.01,   # Acceptable quality level (1%)
  CRQ = 0.05,   # Rejectable quality level (5%)
  alpha = 0.02, # Producer's risk
  beta = 0.15,  # Consumer's risk
  distribution = "binomial"
)

# Summary of the plan
summary(plan_attr)
#> Attributes Acceptance Sampling Plan: 
#>  Distribution: binomial 
#>  Sample Size (n): 144 
#>  Acceptance Number (c): 4 
#>  Producer's Risk (PR = 0.01534843 ) at PRQ = 0.01 
#>  Consumer's Risk (CR = 0.1487162 ) at CRQ = 0.05

# Probability of accepting 3% defective
accProb(plan_attr, 0.03)
#> [1] 0.5656415

# Plot the OC curve
plot(plan_attr)

Variables Sampling Example (Normal Distribution, Known Sigma)

# Create a variable plan assuming known sigma
plan_var <- optPlan(
  PRQ = 0.025,
  CRQ = 0.1,
  alpha = 0.05,
  beta = 0.10,
  distribution = "normal",
  sigma_type = "known"
)

# Summary
summary(plan_var)
#> Variables Acceptance Sampling Plan
#>  Distribution: normal 
#>  Sample Size (n): 19 
#>  Acceptability Constant (k): 1.579 
#>  Population Standard Deviation: known 
#>  Producer's Risk (PR = 0.05 ) at PRQ = 0.025 
#>  Consumer's Risk (CR = 0.1 ) at CRQ = 0.1

# Plot OC curve
plot(plan_var)

Variables Sampling Example (Normal Distribution, Unknown Sigma)

# Create a variable plan assuming known sigma
plan_var2 <- optPlan(
  PRQ = 0.025,
  CRQ = 0.1,
  alpha = 0.05,
  beta = 0.10,
  distribution = "normal",
  sigma_type = "unknown"
)

# Summary
summary(plan_var2)
#> Variables Acceptance Sampling Plan
#>  Distribution: normal 
#>  Sample Size (n): 43 
#>  Acceptability Constant (k): 1.586 
#>  Population Standard Deviation: unknown 
#>  Producer's Risk (PR = 0.05 ) at PRQ = 0.025 
#>  Consumer's Risk (CR = 0.1 ) at CRQ = 0.1

Variables Sampling Example (Beta Distribution, Known Theta)

# Create a variable plan using Beta distribution
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
summary(plan_beta)
#> Variables Acceptance Sampling Plan
#>  Distribution: beta 
#>  Sample Size (n): 14 
#>  Acceptability Constant (k): 1.186 
#>  Population Precision Parameter (theta): known 
#>  Producer's Risk (PR = 0.04999589 ) at PRQ = 0.05 
#>  Consumer's Risk (CR = 0.09947491 ) at CRQ = 0.2 
#>  Lower Specification Limit (LSL): 1e-05

# Plot OC curve
plot(plan_beta)

# Plot OC curve be the process mean
plot(plan_beta, by = "mean")

Variables Sampling Example (Beta Distribution, Unknown Theta)

# Create a variable plan using Beta distribution
plan_beta2 <- optPlan(
  PRQ = 0.05,
  CRQ = 0.2,
  alpha = 0.05,
  beta = 0.10,
  distribution = "beta",
  theta = 44000000,
  theta_type = "unknown",
  LSL = 0.00001
)

# Summary
summary(plan_beta2)
#> Variables Acceptance Sampling Plan
#>  Distribution: beta 
#>  Sample Size (n): 31 
#>  Acceptability Constant (k): 1.186 
#>  Population Precision Parameter (theta): unknown 
#>  Producer's Risk (PR = 0.04735398 ) at PRQ = 0.05 
#>  Consumer's Risk (CR = 0.09598793 ) at CRQ = 0.2 
#>  Lower Specification Limit (LSL): 1e-05

Custom Plan Comparison

# Define range of defect rates
pd <- seq(0, 0.15, by = 0.001)

# Generate OC data from optimal plan
oc_opt <- OCdata(plan = plan_attr, pd = pd)

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

# Plot comparison
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 vignette 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). Single Sampling Plans for Inspection by Variables under a Variance Component Situation. In Frontiers in Statistical Quality Control 7.
Govindaraju, K., & Kissling, R. (2015). Sampling plans for Beta-distributed compositional fractions. Quality Engineering, 27(1), 1–13.

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.