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LGCU: Learning Gamma CUSUM
Overview
LGCU (Learning Gamma CUSUM) is an R package for designing and analyzing CUSUM control charts applied to Gamma distributions with guaranteed performance. The package provides methods for:
- Estimating Average Run Length (ARL) for both upward and downward CUSUM charts.
- Visualizing CUSUM control charts for process monitoring.
- Calibrating control limits using Monte Carlo simulations.
- Applying cautious learning mechanisms to dynamically update parameters.
The methodologies implemented follow the work of Madrid-Alvarez, García-Díaz, and Tercero-Gómez (2024), ensuring rigorous statistical foundations and practical applications in industrial quality control.
Installation
To install the package from GitHub:
# Install devtools if not already installed
install.packages("devtools")
# Install LGCU from GitHub
devtools::install_github("your_github_username/LGCU")To load the package:
library(LGCU)Functions & Usage
1. ARL Estimation for CUSUM Control Charts
Downward CUSUM ARL Calculation (Guaranteed Performance)
GICARL_CUSUM_down(alpha, beta, alpha_est, beta_est, beta_ratio, H_minus, H_delta, m)
# Example:
GICARL_CUSUM_down(alpha = 1, beta = 1, alpha_est = 1, beta_est = 1,
beta_ratio = 1/2.5, H_minus = -2.792, H_delta = 0, m = 100)Upward CUSUM ARL Calculation (Guaranteed Performance)
GICARL_CUSUM_up(alpha, beta, alpha_est, beta_est, beta_ratio, H_plus, H_delta, m)
# Example:
GICARL_CUSUM_up(alpha = 1, beta = 1, alpha_est = 1.2, beta_est = 0.8,
beta_ratio = 2, H_plus = 6.5081, H_delta = 2.9693, m = 100)Downward CUSUM ARL Calculation (With Learning)
ARL_Clminus(alpha, beta, alpha0_est, beta0_est, known_alpha, beta_ratio, H_delta, H_minus, n_I, replicates, K_l, delay, tau)
# Example:
ARL_Clminus(
alpha = 1,
beta = 1,
alpha0_est = 1.067, # alpha = known_alpha
beta0_est = 0.2760, # Estimated Beta
known_alpha = TRUE,
beta_ratio = 1/2,
H_delta = 0.6946,
H_minus = -4.8272,
n_I = 500,
replicates = 1000,
K_l = 0.5,
delay = 25,
tau = 1
)Upward CUSUM ARL Calculation (With Learning)
ARL_Clplus(alpha, beta, alpha0_est, beta0_est, known_alpha, beta_ratio, H_delta, H_plus, n_I, replicates, K_l, delay, tau)
# Example:
ARL_Clplus(
alpha = 1,
beta = 1,
alpha0_est = 1, # alpha = known_alpha
beta0_est = 1.1, # Estimated Beta
known_alpha = TRUE,
beta_ratio = 2,
H_delta = 4.2433,
H_plus = 8.7434,
n_I = 200,
replicates = 100,
K_l = 2,
delay = 25,
tau = 1
)2. CUSUM Control Chart Visualization
Downward CUSUM Chart
plot_GICCdown_chart(alpha, beta, beta_ratio, H_delta, H_minus, n_I, n_II, faseI, faseII, known_alpha)
# Example:
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)Upward CUSUM Chart
plot_GICCup_chart(alpha, beta, beta_ratio, H_delta, H_plus, n_I, n_II, faseI, faseII, known_alpha)
# Example:
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)Bidirectional CUSUM Chart
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, faseII, known_alpha)
# Example:
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)3. CUSUM Chart with Learning Mechanism
Downward CUSUM with Learning
plot_GICCLdown_Chart(alpha, beta, beta_ratio, H_delta, H_minus, known_alpha, k_l, delay, tau, n_I, n_II, faseI, faseII)
# Example:
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 = NULL, faseII = NULL)Upward CUSUM with Learning
plot_GICCLup_Chart(alpha, beta, beta_ratio, H_delta, H_plus, known_alpha, k_l, delay, tau, n_I, n_II, faseI, faseII)
# Example:
plot_GICCLup_Chart(alpha = 1, beta = 1, beta_ratio = 2, H_delta = 2.9819, H_plus = 6.5081,
known_alpha = TRUE, k_l = 2, delay = 25, tau = 1,
n_I = 200, n_II = 710, faseI = NULL, faseII = NULL)Bidirectional CUSUM with Learning
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, faseII)
# Example:
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)4. Calibration of H_delta for Guaranteed Performance
Downward Calibration
getDeltaH_down(n_I, alpha, beta, beta_ratio, H_minus, a, b, ARL_esp, m, N_init, N_final, known_alpha)
# Example:
getDeltaH_down(n_I = 100, alpha = 1, beta = 1, beta_ratio = 1/2, H_minus = -4.1497,
a = 0.1, b = 0.05, ARL_esp = 370, m = 100, N_init = 10, N_final = 1000, known_alpha = TRUE)Upward Calibration
getDeltaH_up(n_I, alpha, beta, beta_ratio, H_plus, a, b, ARL_esp, m, N_init, N_final, known_alpha)
# Example:
getDeltaH_up(n_I = 100, alpha = 1, beta = 1, beta_ratio = 2, H_plus = 6.8313,
a = 0.1, b = 0.05, ARL_esp = 370, m = 100, N_init = 10, N_final = 1000, known_alpha = TRUE)5. Calibration of H_delta with Learning
Downward Calibration with Learning
getDeltaHL_down(n_I, alpha, beta, beta_ratio, H_minus, a, b, ARL_esp, replicates, N_init, N_final, known_alpha, K_l, delay, tau)
# Example:
getDeltaHL_down(n_I = 200, alpha = 1, beta = 1, beta_ratio = 1/1.5,
H_minus = -6.2913, a = 0.1, b = 0.05, ARL_esp = 370,
replicates = 10, N_init = 100, N_final = 1000, known_alpha = TRUE,
K_l = 0.7, delay = 25, tau = 1)Upward Calibration with Learning
getDeltaHL_up(n_I, alpha, beta, beta_ratio, H_plus, a, b, ARL_esp, replicates, N_init, N_final, known_alpha, K_l, delay, tau)
# Example:
getDeltaHL_up(n_I = 200, alpha = 1, beta = 1, beta_ratio = 2,
H_plus = 6.8313, a = 0.1, b = 0.05, ARL_esp = 370,
replicates = 100, N_init = 100, N_final = 500, known_alpha = TRUE,
K_l = 2, delay = 25, tau = 1)