plot_GICC_chart2: CUSUM Control Chart for Gamma Distribution with Guaranteed...

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

CUSUM Control Chart for Gamma Distribution with Guaranteed Performance

Description

This function generates a bidirectional (upward and downward) CUSUM control chart for a Gamma distribution, allowing the monitoring of the evolution of the CUSUM statistic while ensuring optimal performance in detecting process changes.

Based on the methodology proposed by Madrid‐Alvarez, García‐Díaz, and Tercero‐Gómez (2024), this implementation employs a Monte Carlo-based approach to estimate the Gamma distribution parameters and determine control limits with precise calibration. The function enables visualization of process evolution and the detection of deviations with reduced risk of false alarms.

Features:

• Implements Monte Carlo simulations for control chart calibration.

• Allows the use of known Gamma distribution values or estimation in Phase I.

• Provides a graphical representation of the CUSUM statistic evolution with guaranteed performance.

• Includes control limits and a legend with key configuration details of the control chart.

For additional details on selecting parameters H_plus, H_minus, H_delta_plus, and H_delta_minus, as well as calibration strategies, it is recommended to consult 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.

Usage

plot_GICC_chart2(
  alpha,
  beta,
  beta_ratio_plus,
  beta_ratio_minus,
  H_delta_plus,
  H_plus,
  H_delta_minus,
  H_minus,
  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_plus	Ratio between beta and its estimation for upward detection.
beta_ratio_minus	Ratio between beta and its estimation for downward detection.
H_delta_plus	Increment of the upper GIC limit.
H_plus	Initial upper limit of the CUSUM chart.
H_delta_minus	Increment of the lower GIC limit.
H_minus	Initial lower 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 showing the evolution of the CUSUM statistic for a Gamma distribution with guaranteed performance, 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 predefined sample sizes
plot_GICC_chart2(alpha = 1, beta = 1, beta_ratio_plus = 2,
                      beta_ratio_minus = 0.5,H_delta_plus = 2.0,
                      H_plus = 5.0, H_delta_minus = 1.5, H_minus = -4.5,
                      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_GICC_chart2(alpha = 1, beta = 1, beta_ratio_plus = 2,
                 beta_ratio_minus = 0.5, H_delta_plus = 2.0, H_plus = 5.0,
                 H_delta_minus = 1.5, H_minus = -4.5, 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.