plot_GICCLdown_Chart: Downward CUSUM Control Chart with Cautious Learning and...

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

Downward CUSUM Control Chart with Cautious Learning and Guaranteed Performance

Description

This function generates a downward CUSUM control chart for a Gamma distribution, incorporating a cautious parameter updating mechanism based on guaranteed performance.

It enables dynamic process monitoring, ensuring progressive adaptation to changes in the distribution.

This approach follows the methodology presented in the work of Madrid-Alvarez, García-Díaz, and Tercero-Gómez (2024), where a cautious learning scheme for parameter updating in CUSUM control charts applied to Gamma distributions is proposed.

The implementation captures changes in the distribution and adjusts the control limits to enhance the detection of process variations.

Features:

• If the user does not provide Phase I and Phase II data, the function generates them automatically.

• If known_alpha = TRUE, alpha is fixed and not estimated.

• If known_alpha = FALSE, alpha is estimated from Phase I data.

• Dynamic control limits and a summary of parameters are included.

• Integrates a cautious learning scheme using the parameters k_l, delay, and tau.

Recommendations

The parameters k_l, delay, and tau are part of the cautious learning mechanism of the CUSUM chart. These values enable the dynamic updating of beta0_est and H_minus, ensuring that the control chart progressively adapts to process changes, improving sensitivity in detecting deviations.

For proper implementation, it is recommended to reference the values proposed in:

Madrid-Alvarez, H. M., García-Díaz, J. C., & Tercero-Gómez, V. G. (2024). A CUSUM control chart for the Gamma distribution with cautious parameter learning. Quality Engineering, 1-23.

While these parameters have been tested and validated in the referenced article, users can adjust them based on the specific characteristics of their process, considering factors such as system variability and desired update frequency.

Additionally, if detailed guidance on selecting values for H_delta and H_minus is needed, it is recommended to review the referenced article, which presents calibration and adjustment strategies for these limits to ensure optimal control chart performance.

Usage

plot_GICCLdown_Chart(
  alpha,
  beta,
  beta_ratio,
  H_delta,
  H_minus,
  known_alpha,
  k_l,
  delay,
  tau,
  n_I,
  n_II,
  faseI = NULL,
  faseII = NULL
)

Arguments

alpha	Shape parameter of the Gamma distribution (if alpha_conocido = TRUE).
beta	Scale parameter of the Gamma distribution.
beta_ratio	Ratio between beta and its estimation.
H_delta	Increment of the lower control limit.
H_minus	Initial lower control limit of the CUSUM chart.
known_alpha	Indicates whether alpha is known (TRUE) or should be estimated (FALSE).
k_l	Secondary control threshold used in the learning logic.
delay	Number of observations before updating beta0_est and H_minus_c.
tau	Time point at which the beta parameter changes.
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 internally.
faseII	Data sample from Phase II (numeric vector). If NULL, it is generated internally.

Value

A plot showing the evolution of the downward CUSUM statistic with cautious learning, including:

• The dynamically adjusted accumulated values of the CUSUM statistic.

• Progressively updated control limits with guaranteed performance.

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

Examples

# Option 1: Providing Phase I and Phase II data
phaseI_data <- rgamma(n = 200, shape = 1, scale = 1)
phaseII_data <- rgamma(n = 710, shape = 1, scale = 1)
plot_GICCLdown_Chart(alpha = 1, beta = 1, beta_ratio = 1/2, H_delta = 4.2433,
                     H_minus= -4.8257, known_alpha = FALSE, k_l = 0.739588,
                     delay = 25, tau = 1, n_I = 200, n_II = 700,
                     faseI = phaseI_data, faseII = phaseII_data)

# Option 2: Without providing data, the function automatically generates them
plot_GICCLdown_Chart(alpha = 1, beta = 1, beta_ratio = 1/2, H_delta = 1.6763,
                     H_minus = -4.8257, known_alpha = FALSE, k_l = 0.739588,
                     delay = 25, tau = 1, n_I = 200,
                     n_II = 710, faseI = NULL, faseII = NULL)

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