| Title: | Beta Control Charts |
| Version: | 1.5 |
| Description: | Applies Beta Control Charts to defined values. The Beta Chart presents control limits based on the Beta probability distribution, making it suitable for monitoring fraction data from a Binomial distribution as a replacement for p-Charts. The Beta Chart has been applied in three real studies and compared with control limits from three different schemes. The comparative analysis showed that: (i) the Beta approximation to the Binomial distribution is more appropriate for values confined within the [0, 1] interval; and (ii) the proposed charts are more sensitive to the average run length (ARL) in both in-control and out-of-control process monitoring. Overall, the Beta Charts outperform the Shewhart control charts in monitoring fraction data. For more details, see Ângelo Márcio Oliveira Sant’Anna and Carla Schwengber ten Caten (2012) <doi:10.1016/j.eswa.2012.02.146>. |
| License: | GPL-3 |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.2.3 |
| NeedsCompilation: | no |
| Packaged: | 2024-06-09 18:47:29 UTC; danie |
| Author: | Ângelo Santanna [aut], Daniel Cerqueira [aut, cre] |
| Maintainer: | Daniel Cerqueira <danielcerqueira@live.com> |
| Repository: | CRAN |
| Date/Publication: | 2024-06-10 17:40:06 UTC |
Apply Shewhart Control Rules
Description
Identifies points in a control chart that violate Shewhart control rules. These rules help to determine if a process is out of control and requires corrective action.
Usage
apply_shewhart_rules(data, limits, type, sizes = NULL)
Arguments
data |
A numeric vector of data values to be analyzed. |
limits |
A list containing the control limits, specifically the lower control limit (LCL) and upper control limit (UCL). |
type |
An integer representing the type of control chart. There are two possible types: |
sizes |
An optional numeric vector of sample sizes. This parameter is typically required for type 1 charts. |
Value
A vector of indices corresponding to data points that violate the Shewhart control rules.
Examples
# Example with discrete data
data_values <- c(0.1, 0.2, 0.15, 0.3, 0.25)
sample_limits <- list(lcl=0.05, ucl=0.25, center=0.15)
apply_shewhart_rules(data_values, sample_limits, type=1)
# Example with continuous data
data_values <- c(0.55, 0.60, 0.65, 0.70, 0.75)
sample_limits <- list(lcl=0.50, ucl=0.70, center=0.60)
apply_shewhart_rules(data_values, sample_limits, type=2)
Beta Control Charts
Description
Creates and displays a Beta control chart using the specified data, sample sizes, and type. This is the main function for generating control charts in this package.
Usage
bcc(data, sizes = NULL, type, title = NULL)
Arguments
data |
A numeric vector of data values to be plotted on the control chart. |
sizes |
An optional numeric vector of sample sizes. This parameter is required for type 1 charts, which are designed for discrete data. |
type |
An integer representing the type of control chart. There are two possible types: |
title |
An optional string specifying the title of the plot. |
Details
The Beta Chart presents control limits based on the Beta probability distribution. It is used for monitoring fraction data from a Binomial distribution as a replacement for p-Charts. The Beta Chart has been applied in three real studies, demonstrating its effectiveness. Comparative analysis revealed that: (i) the Beta approximation to the Binomial distribution is more appropriate for values confined within the [0, 1] interval; and (ii) the proposed charts are more sensitive to the average run length (ARL) in both in-control and out-of-control process monitoring. Overall, the Beta Charts outperform the Shewhart control charts for monitoring fraction data.
Value
A plot of the Beta control chart.
Examples
# Example for type 1 chart with discrete data
data <- c(0.12, 0.18, 0.14, 0.28, 0.22)
sizes <- c(101, 98, 110, 105, 95)
bcc(data, sizes, type=1, title="Beta Control Chart for Discrete Data")
# Example for type 2 chart with continuous data
data <- c(0.59, 0.67, 0.61, 0.70, 0.59)
bcc(data, type=2, title="Beta Control Chart for Continuous Data")
# Example changing the title of the chart
data <- c(0.07, 0.13, 0.21, 0.25, 0.19)
sizes <- c(52, 49, 51, 53, 48)
bcc(data, sizes, type=1, title="Custom Title: Beta Control Chart for Discrete Data")
Calculate Control Limits
Description
Calculates control limits for control charts using given data and sizes. Supports both type 1 (discrete data) and type 2 (continuous data) control charts.
Usage
calculate_limits(data, sizes = NULL, type)
Arguments
data |
A numeric vector of data values. |
sizes |
An optional numeric vector of sample sizes. Required for type 1 charts. |
type |
An integer representing the type of control chart. There are two possible types: |
Value
A list containing the lower and upper control limits, and the center.
Examples
# Example for type 2 chart with continuous data
data_values <- c(0.55, 0.60, 0.65, 0.70, 0.75)
calculate_limits(data_values, type=2)
Plot Control Chart
Description
Generates and plots a control chart using the given data, sizes, type, and control limits.
Usage
plot_control_chart(data, type, limits, title, sizes = NULL)
Arguments
data |
A numeric vector of data values. |
type |
An integer representing the type of control chart (either 1 or 2). |
limits |
A list containing the lower and upper control limits, and the center. |
title |
A string for the plot title. |
sizes |
A numeric vector of sample sizes. |
Value
A plot of the control chart.
Examples
data <- c(0.12, 0.18, 0.14, 0.28, 0.22)
sizes <- c(101, 98, 110, 105, 95)
limits <- list(lcl = 4.03915, ucl = 16.0, center = 0.216)
plot_control_chart(data, type=1, limits=limits, title="Sample Control Chart", sizes=sizes)