AccSamplingDesign: Acceptance Sampling Plan Design - R Package

Ha Truong

2025-11-16

1 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:

Install from CRAN:

install.packages("AccSamplingDesign")

Or from GitHub:

devtools::install_github("vietha/AccSamplingDesign")

2 Attributes Sampling Examples

# 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)

3 Variables Sampling Examples

3.1 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, rounded up): 19  [raw n = 18.60721 ]
#>  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)

3.2 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, rounded up): 43  [raw n = 42.67339 ]
#>  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

3.3 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, rounded up): 14  [raw n = 13.05195 ]
#>  Acceptability Constant (k): 1.188 
#>  Population Precision Parameter (theta): known 
#>  Producer's Risk (PR = 0.05412522 ) at PRQ = 0.05 
#>  Consumer's Risk (CR = 0.1025498 ) 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")

3.4 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, rounded up): 31  [raw n = 30.79007 ]
#>  Acceptability Constant (k): 1.188 
#>  Population Precision Parameter (theta): unknown 
#>  Producer's Risk (PR = 0.04808494 ) at PRQ = 0.05 
#>  Consumer's Risk (CR = 0.09474857 ) at CRQ = 0.2 
#>  Lower Specification Limit (LSL): 1e-05

3.5 Variables Sampling Plan Output Note

When designing a variables acceptance sampling plan using optPlan() or optVarPlan(),
the returned object includes two related quantities for the sample size:

Example:

plan_beta2$sample_size  # integer sample size used in plan
#> [1] 31
plan_beta2$n            # raw computed (non-rounded) value
#> [1] 30.79007

3.6 Estimating θ for Beta-Based Plans

For Beta-distributed quality characteristics, the precision parameter θ reflects the concentration of the distribution around the mean. If θ is unknown, it can be estimated from historical process data.

A practical approach is to use the VGAM package, which provides the betaff function for fitting a Beta distribution and obtaining θ:

# Example data
y <- c(0.75, 0.68, 0.72, 0.70, 0.76)

# Fit Beta model
fit <- vglm(y ~ 1, betaff, data = data.frame(y = y))

# Extract estimated parameters
coef(fit, matrix = TRUE)
#>             logitlink(mu) loglink(phi)
#> (Intercept)     0.9544037     5.410654

The output provides estimates of the mean (μ) and the precision parameter (θ). Use the estimated θ directly in optPlan(), e.g.:

theta_est <- exp(coef(fit, matrix = TRUE)[1, "loglink(phi)"])
theta_est
#> [1] 223.7778
optPlan(PRQ = 0.05, CRQ = 0.20, alpha = 0.05, beta = 0.10,
           USL = 0.8, distribution = "beta", theta_type = "unknown",
           theta = theta_est)
#> VarPlan object:
#>  Distribution: beta 
#>  Theta type: unknown 
#>  Sample size (n): 31 
#>  Acceptability constant (k): 1.179908 
#> 
#> NOTE: summary(plan) for detail report, 
#>       plot(plan) for quick OC visualization, 
#>       OCdata(plan) to extract data for evaluation and custom plots.

3.7 Optimization Approach for Sampling Plans

The AccSamplingDesign package determines optimal sample sizes and acceptance criteria for variable sampling plans via numerical optimization.

This approach ensures stable and efficient plan calculations while relying solely on base R functionality, avoiding additional package dependencies.

4 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)

5 References

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: