Generic function for OC Curve Generation

Description

Generic function to compute Operating Characteristic (OC) curve data from an acceptance sampling plan.

Usage

OCdata(plan, pd = NULL)

Arguments

Details

This is a generic function. Methods are defined for objects of class AttrPlan and VarPlan, which compute the probability of acceptance across a range of quality levels (proportions of nonconforming).

See OCdata.AttrPlan and OCdata.VarPlan for details.

Value

An object of class "OCdata", a list containing:

• pd — quality levels (e.g. proportion defective)

• paccept — probability of acceptance at each level

• process_means — process means, if applicable

• dist, n, k, c — plan parameters

Author(s)

Ha Truong

See Also

optPlan, manualPlan

Acceptance Probability

Description

Calculate the probability of acceptance for a given quality level.

Usage

accProb(plan, p)

Arguments

Value

Numeric probability between 0 and 1.

Author(s)

Ha Truong

Examples

# Example for attribute plan
attr_plan <- optAttrPlan(PRQ = 0.01, CRQ = 0.1)
accProb(attr_plan, 0.05)

# Example for variable plan (normal distribution)
var_plan <- optVarPlan(
  PRQ = 0.025,        # Acceptable quality level (% nonconforming)
  CRQ = 0.1,         # Rejectable quality level (% nonconforming)
  alpha = 0.05,      # Producer's risk
  beta = 0.1,        # Consumer's risk
  distribution = "normal"
)
accProb(var_plan, 0.05)

Create manual acceptance sampling (AS) plan from User Inputs

Description

Constructs an AttrPlan or VarPlan object from the given parameters.

Usage

manualPlan(distribution = c("binomial", "poisson", "normal", "beta"),
           n = NULL, c = NULL, k = NULL,
           USL = NULL, LSL = NULL, sigma = NULL, theta = NULL,
           sigma_type = c("known", "unknown"),
           theta_type = c("known", "unknown"))

Arguments

Details

This function provides a user-friendly wrapper to construct AS plan directly from parameters. Internally, it constructs the appropriate AttrPlan or VarPlan, from given paramenters.

Value

An object of class "AttrPlan" or VarPlan.

Author(s)

Ha Truong

See Also

optPlan, OCdata

Examples

# Attribute sampling with user-defined parameters
plan1 <- manualPlan(n = 100, c = 2, distribution = "binomial")

# Variable sampling (normal)
plan2 <- manualPlan(n = 30, k = 1.5, distribution = "normal", USL = 10, sigma = 1)

Estimate Mean \mu Based on Specification Limits and Probability

Description

Computes the estimated mean \mu for a given level of quality and specification limit under either a normal or beta distribution.

Usage

muEst(p, USL = NULL, LSL = NULL, 
       sigma = NULL, theta = NULL, 
       dist = c("normal", "beta"))

Arguments

Details

The function estimates the mean \mu corresponding to a given tail probability p, assuming that the process output follows either a normal or beta distribution, and that the probability of being beyond the provided specification limit equals 1 - p.

• For the normal distribution, the mean is calculated using the inverse cumulative distribution function (quantile function) of the normal distribution.

• For the beta distribution, the mean is solved numerically such that the CDF at the specified limit equals p, given the shape determined by theta.

Exactly one of USL or LSL must be provided to define whether the probability refers to the upper or lower tail.

Value

Returns the estimated mean \mu as a numeric value.

Author(s)

Ha Truong

Examples

  # Example for normal distribution with lower specification limit (LSL)
  muEst(p = 0.95, LSL = 10, sigma = 2, dist = "normal")

  # Example for beta distribution with upper specification limit (USL)
  muEst(p = 0.95, USL = 0.7, theta = 500, dist = "beta")

Attribute Acceptance Sampling Plan

Description

Designs binomial-based acceptance sampling plans using producer/consumer risk criteria.

Usage

optAttrPlan(PRQ, CRQ, alpha = 0.05, beta = 0.10, 
            distribution = c("binomial", "poisson"))

Arguments

Value

AttrPlan object containing:

Author(s)

Ha Truong

References

ISO 2859-1:1999 - Sampling procedures for inspection by attributes

Schilling, E.G., & Neubauer, D.V. (2017). Acceptance Sampling in Quality Control (3rd ed.). Chapman and Hall/CRC. https://doi.org/10.4324/9781315120744

Examples

plan <- optAttrPlan(PRQ = 0.01, CRQ = 0.1, alpha = 0.05, beta = 0.1, 
                    distribution = "binomial")

Optimal Acceptance Sampling Plan

Description

Design optimal variable acceptance sampling plans based on specified parameters. Supports different distributions (binomial, normal, beta) and accommodates known or unknown standard deviation and process parameters.

Usage

optPlan(PRQ, CRQ, alpha = 0.05, beta = 0.10, USL = NULL, LSL = NULL,
        distribution = c("binomial", "poisson", "normal", "beta"),
        sigma_type = c("known", "unknown"),
        theta_type = c("known", "unknown"),
        sigma = NULL, theta = NULL)

Arguments

Details

This function designs optimal acceptance sampling plans by balancing producer's and consumer's risks under specified quality levels. It supports plans for attributes (binomial) and variables (normal or beta distributions), including cases with unknown standard deviation or distributional parameters.

Value

Returns a list or data frame with optimal sample size(s) and critical value(s) based on the specified parameters and distribution.

Author(s)

Ha Truong

Examples

# Example usage (normal distribution, known sigma):
optPlan(PRQ = 0.005, CRQ = 0.03, alpha = 0.05, beta = 0.10, 
        distribution = "normal", sigma_type = "known")

# Example usage (beta distribution, unknown theta):
optPlan(PRQ = 0.025, CRQ = 0.10, alpha = 0.05, beta = 0.10, 
        distribution = "beta", theta = 6.6e8, 
        theta_type = "unknown", LSL = 5.65e-6)

Variable Acceptance Sampling Plan

Description

Creates variable sampling plans for normal or beta distributed measurements.

Usage

optVarPlan(PRQ, CRQ, alpha = 0.05, beta = 0.10, USL = NULL, LSL = NULL,
           distribution = c("normal", "beta"), sigma_type = c("known", "unknown"),
           theta_type = c("known", "unknown"), sigma = NULL, theta = NULL)

Arguments

Details

The function generates variable acceptance sampling plans based on specified producer and consumer risks and either a normal or beta distribution model.

The specification limit must be defined via either USL (upper specification limit) or LSL (lower specification limit), depending on whether the one-sided quality criterion concerns the upper or lower tail. Only one limit should be provided.

The plan design accounts for known or unknown standard deviation in the normal case, and known or unknown dispersion parameter (theta) in the beta case. Measurement error, if any, can be incorporated via the measurement_error argument.

Value

A VarPlan object containing:

Author(s)

Ha Truong

References

ISO 3951-1:2013 - Sampling procedures for inspection by variables.

Wilrich, PT. (2004). Single Sampling Plans for Inspection by Variables under a Variance Component Situation. In: Lenz, HJ., Wilrich, PT. (eds) Frontiers in Statistical Quality Control 7. Physica, Heidelberg. doi:10.1007/978-3-7908-2674-6_4

K. Govindaraju and R. Kissling (2015). Sampling plans for Beta-distributed compositional fractions.

Examples

# Example for normal distribution plan
norm_plan <- optVarPlan(
  PRQ = 0.025,        # Acceptable quality level (% nonconforming)
  CRQ = 0.1,          # Rejectable quality level (% nonconforming)
  alpha = 0.05,       # Producer's risk
  beta = 0.1,         # Consumer's risk
  distribution = "normal",
  USL = 10
)
summary(norm_plan)

# Example for beta distribution plan
beta_plan <- optVarPlan(
  PRQ = 0.025,        # Target quality level (% nonconforming)
  CRQ = 0.1,          # Minimum quality level (% nonconforming)
  alpha = 0.05,       # Producer's risk
  beta = 0.1,         # Consumer's risk
  distribution = "beta",
  theta = 44000000,   # Beta distribution parameter
  LSL = 0.00001
)
summary(beta_plan)

Plot the OC Curve for Attribute Sampling Plans

Description

Plots the Operating Characteristic (OC) curve for an attribute sampling plan object of class AttrPlan.

Usage

## S3 method for class 'AttrPlan'
plot(x, pd = NULL, ...)

Arguments

Details

This method computes and visualizes the probability of acceptance (P(accept)) as a function of the proportion of nonconforming items in the population, based on the attribute sampling plan.

The plot also includes reference lines at the plan's producer and consumer quality levels (PRQ, CRQ) and their corresponding acceptance probabilities.

Value

A plot showing the OC curve for the given attribute sampling plan.

Author(s)

Ha Truong

See Also

optAttrPlan, accProb, OCdata

Examples

# Create attribute plan
plan <- optAttrPlan(PRQ = 0.01, CRQ = 0.1)

# Plot OC curve
plot(plan)

# With custom pd
plot(plan, pd = seq(0, 0.15, by = 0.001))

Plot Method for OCdata Objects

Description

Plots the Operating Characteristic (OC) curve from an object of class "OCdata", either by proportion nonconforming or process mean levels.

Usage

## S3 method for class 'OCdata'
plot(x, by = c("pd", "mean"), ...)

Arguments

Details

This method visualizes the OC curve based on the content of the "OCdata" object.

By default, the curve is plotted against the proportion of nonconforming items (@pd). If by = "mean" is specified and the plan includes valid mean-level estimates (@process_means), the curve is plotted against mean levels.

If by = "mean" is requested but no mean estimates are available (e.g., for attribute plans), a message will be shown and no plot will be drawn.

Value

A plot showing the OC curve for the given attribute/variable sampling plan.

Author(s)

Ha Truong

See Also

OCdata, optAttrPlan, optVarPlan

Examples

# Attribute plan
plan_attr <- optAttrPlan(PRQ = 0.01, CRQ = 0.05)
oc_attr <- OCdata(plan_attr)
plot(oc_attr)               # OC curve by pd (default)
plot(oc_attr, by = "mean")  # Will show message if not available

# Variable plan
plan_var <- optVarPlan(PRQ = 0.025, CRQ = 0.1, USL = 0.1,
                       distribution = "normal", sigma=0.01)
oc_var <- OCdata(plan_var)
plot(oc_var)                # OC curve by pd
plot(oc_var, by = "mean")   # OC curve by mean levels

Plot the OC Curve for Variable Sampling Plans

Description

Plots the Operating Characteristic (OC) curve for an object of class VarPlan. Supports plotting against either the proportion of nonconforming items or the corresponding process mean levels, depending on availability.

Usage

## S3 method for class 'VarPlan'
plot(x, pd = NULL, by = c("pd", "mean"), ...)

Arguments

Details

This plotting method visualizes the probability of acceptance (P(accept)) against the desired metric, based on the parameters of a variable sampling plan.

If by = "pd", the x-axis represents the proportion of nonconforming items. If by = "mean" and the plan defines limit_type and spec_limit, the function estimates corresponding process means using muEst and plots the OC curve by those mean values.

Reference lines for the Producer's Risk Quality (PRQ) and Consumer's Risk Quality (CRQ), along with their respective acceptance probabilities, are shown when plotting by proportion.

Value

A plot showing the OC curve for the given variable sampling plan, either by nonconforming proportion or mean level.

Author(s)

Ha Truong

See Also

optVarPlan, accProb, muEst, OCdata, plot.OCdata

Examples

# Variable sampling plan with specification limits
plan <- optVarPlan(
  PRQ = 0.025, CRQ = 0.1,
  alpha = 0.05, beta = 0.1,
  distribution = "normal",
  USL = 3, sigma = 0.1
)

# Plot by proportion nonconforming
plot(plan, by = "pd")

# Plot by estimated mean level (requires spec_limit and limit_type)
plot(plan, by = "mean")

# Custom pd vector
plot(plan, pd = seq(0.01, 0.15, by = 0.001))

Summarize Attribute Acceptance Plan

Description

Detailed summaries for attribute acceptance plans.

Usage

## S3 method for class 'AttrPlan'
summary(object, ...)

Arguments

Value

No return value. This function is called for its side effect of printing a formatted summary of the attribute sampling plan to the console.

Author(s)

Ha Truong

Examples

attr_plan <- optAttrPlan(PRQ = 0.01, CRQ = 0.1)
summary(attr_plan)

Summarize Variable Acceptance Plan

Description

Detailed summaries for variable acceptance plans.

Usage

## S3 method for class 'VarPlan'
summary(object, ...)

Arguments

Value

No return value. This function is called for its side effect of printing a formatted summary of the variable sampling plan to the console.

Author(s)

Ha Truong

Examples

var_plan <- optVarPlan(
  PRQ = 0.025,       # Acceptable quality level (% nonconforming)
  CRQ = 0.1,         # Rejectable quality level (% nonconforming)
  alpha = 0.05,      # Producer's risk
  beta = 0.1,        # Consumer's risk
  distribution = "normal"
)
summary(var_plan)