LGCU (version 0.1.5)

plot_GICCL_chart2: CUSUM Control Chart with Cautious Learning and Guaranteed Performance

Description

This function generates a bidirectional (upward and downward) CUSUM control chart for a Gamma distribution, incorporating a cautious parameter update mechanism with guaranteed performance. Its purpose is to enhance sensitivity and precision in detecting changes in dynamic processes.

Based on the methodology presented by Madrid-Alvarez, García-Díaz, and Tercero-Gómez (2024), this implementation allows control limits to adapt according to the evolution of the process, ensuring early detection of variations while minimizing the risk of false alarms.

Features:

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

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

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

• Includes dynamic control limits and a summary table of parameters.

• Enables the detection of both upward and downward deviations, progressively adjusting the control limits.

Recommendations

• The parameters k_l, delay, and tau are crucial for the learning process in the control chart. They regulate the progressive update of control limits, allowing the dynamic update of beta0_est, H_plus_c, and H_minus_c, ensuring that the control chart gradually adjusts to changes in the process. It is recommended to use reference values presented 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.

• Similar to the parameters above, for proper selection of H_plus, H_minus, H_delta_plus, and H_delta_minus values, it is recommended to review the reference article, where detailed calibration strategies for different scenarios are presented.

Usage

plot_GICCL_chart2(
  alpha,
  beta,
  beta_ratio_plus,
  beta_ratio_minus,
  H_delta_plus,
  H_plus,
  H_delta_minus,
  H_minus,
  known_alpha,
  k_l,
  delay,
  tau,
  n_I,
  n_II,
  faseI = NULL,
  faseII = NULL
)

Value

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

• 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.

Arguments

alpha

Shape parameter of the Gamma distribution (if known_alpha = TRUE).

beta

Scale parameter of the Gamma distribution.

beta_ratio_plus

Ratio between beta and its estimate for upward detection.

beta_ratio_minus

Ratio between beta and its estimate for downward detection.

H_delta_plus

Increment of the upper control limit.

H_plus

Initial upper limit of the CUSUM chart.

H_delta_minus

Increment of the lower control limit.

H_minus

Initial lower 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, H_plus_c, 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.

Examples

# Option 1: Automatically generated data
plot_GICCL_chart2(alpha = 1, beta = 1,
                 beta_ratio_plus = 2, beta_ratio_minus = 0.5,
                 H_delta_plus = 3.0, H_plus = 6.5,
                 H_delta_minus = 2.0, H_minus = -5.0,
                 known_alpha = TRUE, k_l = 2, delay = 25, tau = 1,
                 n_I = 200, n_II = 700,
                 faseI = NULL, faseII = NULL)

# Option 2: User-provided data
datos_faseI <- rgamma(n = 200, shape = 1, scale = 1)
datos_faseII <- rgamma(n = 700, shape = 1, scale = 1)
plot_GICCL_chart2(alpha = 1, beta = 1,
                 beta_ratio_plus = 2, beta_ratio_minus = 0.5,
                 H_delta_plus = 3.0, H_plus = 6.5,
                 H_delta_minus = 2.0, H_minus = -5.0,
                 known_alpha = FALSE, k_l = 2, delay = 25, tau = 1,
                 n_I = 200, n_II = 700,
                 faseI = datos_faseI, faseII = datos_faseII)