plot_GICCup_chart: Upward CUSUM Control Chart for Gamma Distribution with...

In LGCU: Implementation of Learning Gamma CUSUM (Cumulative Sum) Control Charts

Upward CUSUM Control Chart for Gamma Distribution with Guaranteed Performance

Description

This function generates an upward CUSUM control chart for a Gamma distribution, displaying the evolution of the CUSUM statistic, control limits, and a summary of the parameters.

Based on the approach presented by Madrid‐Alvarez, García‐Díaz, and Tercero‐Gómez (2024), this implementation enables the evaluation and visualization of the monitored process using a CUSUM chart adapted to Gamma distributions with guaranteed performance.

Specifically, the library incorporates a Monte Carlo model for simulating the control chart behavior, allowing the Gamma distribution to be estimated in Phase I or using predefined values. Additionally, it provides a clear graphical representation of the CUSUM statistic's evolution, ensuring proper calibration and process control.

Recommendations

To check specific values for H_delta and H_plus, it is recommended to review the reference article: Madrid‐Alvarez, H. M., García‐Díaz, J. C., & Tercero‐Gómez, V. G. (2024). A CUSUM control chart for gamma distribution with guaranteed performance. Quality and Reliability Engineering International, 40(3), 1279-1301.

Features:

• Based on a Monte Carlo model.

• Estimates the Gamma distribution in Phase I or uses predefined values.

• Plots the accumulated values of the CUSUM statistic with guaranteed performance.

• Includes control limits and a summary table.

Usage

plot_GICCup_chart(
  alpha,
  beta,
  beta_ratio,
  H_delta,
  H_plus,
  n_I,
  n_II,
  faseI = NULL,
  faseII = NULL,
  known_alpha
)

Arguments

alpha	Shape parameter of the Gamma distribution.
beta	Scale parameter of the Gamma distribution.
beta_ratio	Ratio between beta and its estimation.
H_delta	Increment of the upper GIC limit.
H_plus	Initial upper limit of the CUSUM chart.
n_I	Sample size in Phase I (if faseI is not provided).
n_II	Sample size in Phase II (if faseII is not provided).
faseI	Sample data from Phase I (numeric vector). If NULL, it is generated with rgamma().
faseII	Sample data from Phase II (numeric vector). If NULL, it is generated with rgamma().
known_alpha	If TRUE, a known alpha is used; if FALSE, it is estimated.

Value

A plot displaying the evolution of the upward CUSUM statistic, including:

• The accumulated values of the CUSUM statistic.

• Control limits with guaranteed performance.

• A summary of the parameters used in the control chart.

Examples

# Option 1: Automatically generate data with defined sample sizes
plot_GICCup_chart(
                  alpha = 1, beta = 1, beta_ratio = 2, H_delta = 0,
                  H_plus = 5.16, n_I = 100, n_II = 200, faseI = NULL,
                  faseII = NULL, known_alpha = TRUE
                  )

# Option 2: Use custom data
phaseI_data <- rgamma(n = 100, shape = 1, scale = 1)
phaseII_data <- rgamma(n = 200, shape = 1, scale = 1)
plot_GICCup_chart(
                  alpha = 1, beta = 1, beta_ratio = 2, H_delta = 2.9693,
                  H_plus = 6.5081, n_I = 100, n_II = 200,
                  faseI = phaseI_data, faseII = phaseII_data,
                  known_alpha = TRUE
                  )

LGCU documentation built on April 12, 2025, 1:59 a.m.