plot_GICCdown_chart: Downward CUSUM Control Chart for Gamma Distribution with...

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

Downward CUSUM Control Chart for Gamma Distribution with Guaranteed Performance

Description

This function generates a downward 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 allows for the evaluation and visualization of monitored processes using a CUSUM chart adapted to Gamma distributions with guaranteed performance.

In particular, the function incorporates a Monte Carlo model to simulate the behavior of the control chart, allowing for the estimation of the Gamma distribution in Phase I or the use of predefined values. Additionally, it provides a clear graphical representation of the evolution of the CUSUM statistic, ensuring appropriate calibration and process control.

Recommendations

To reference specific values of H_delta and H_minus, it is recommended to consult the following 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.

• The Gamma distribution is either estimated in Phase I or predefined values are used.

• Accumulated values of the CUSUM statistic with guaranteed performance are plotted.

• Control limits and a summary table are included.

Usage

plot_GICCdown_chart(
  alpha,
  beta,
  beta_ratio,
  H_delta,
  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	Ratio between beta and its estimation.
H_delta	Increment of the lower control limit (GIC).
H_minus	Initial lower control 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	Data sample from Phase I (numeric vector). If NULL, it is generated using rgamma().
faseII	Data sample from Phase II (numeric vector). If NULL, it is generated using rgamma().
known_alpha	If TRUE, a known alpha is used; if FALSE, it is estimated.

Value

A plot showing the evolution of the downward 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_GICCdown_chart(
                    alpha = 3, beta = 1, beta_ratio = 1/2, H_delta = 0.9596,
                    H_minus = -4.6901,n_I = 100, n_II = 200, faseI = NULL,
                    faseII = NULL, known_alpha = FALSE
                    )

# Option 2: Use custom data
phaseI_data <- rgamma(n = 100, shape = 1, scale = 1)
phaseII_data <- rgamma(n = 200, shape = 1, scale = 1)
plot_GICCdown_chart(
                    alpha = 1, beta = 1, beta_ratio = 1/2, H_delta = 2.9693,
                    H_minus = -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.