plot_GICCL_chart2 {LGCU} | R Documentation |
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
, andtau
are crucial for the learning process in the control chart. They regulate the progressive update of control limits, allowing the dynamic update ofbeta0_est
,H_plus_c
, andH_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
, andH_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
)
Arguments
alpha |
Shape parameter of the Gamma distribution (if |
beta |
Scale parameter of the Gamma distribution. |
beta_ratio_plus |
Ratio between |
beta_ratio_minus |
Ratio between |
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 |
k_l |
Secondary control threshold used in the learning logic. |
delay |
Number of observations before updating |
tau |
Time point at which the |
n_I |
Sample size in Phase I (if |
n_II |
Sample size in Phase II (if |
faseI |
Data sample from Phase I (numeric vector). If |
faseII |
Data sample from Phase II (numeric vector). If |
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.
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)