getDeltaH_up {LGCU} | R Documentation |
Estimation of the optimal H_delta
value to guarantee performance in the upward CUSUM control chart
Description
This function calculates the optimal H_delta
value that ensures specific performance in the Gamma CUSUM
control chart for upward detection. It relies on Monte Carlo simulations and an iterative adjustment process
to determine the appropriate value.
Following the methodology proposed by Madrid-Alvarez, Garcia-Diaz, and Tercero-Gomez (2024),
this function allows adjusting H_delta
for different sample size scenarios, ensuring that the control chart
maintains the expected performance in terms of ARL.
Features:
Implements Monte Carlo simulations to estimate
H_delta
.Based on parameter estimates obtained in Phase I.
Iteratively adjusts
H_delta
until the specified ARL is reached.Displays total execution time using
tictoc
.
Recommendations
This function is useful for estimating
H_delta
values in scenarios where the sample size differs from the values reported in the reference article:Madrid-Alvarez, H. M., Garcia-Diaz, J. C., & Tercero-Gomez, V. G. (2024). A CUSUM control chart for gamma distribution with guaranteed performance. Quality and Reliability Engineering International, 40(3), 1279-1301.
-
The adjustment process is iterative and computationally demanding, as its execution time depends on the number of iterations (
N_init + N_final
) and the sample size (n_I
). It is recommended to establish an appropriate convergence criterion to optimize execution time without compromising the accuracy of
H_delta
estimation.For selecting values of
H_plus
,a
, andb
, refer to the reference article, which presents specific strategies and recommendations for calibration.
Usage
getDeltaH_up(
n_I,
alpha,
beta,
beta_ratio,
H_plus,
a,
b,
ARL_esp,
m,
N_init,
N_final,
known_alpha
)
Arguments
n_I |
Sample size in Phase I. |
alpha |
Shape parameter of the Gamma distribution. |
beta |
Scale parameter of the Gamma distribution. |
beta_ratio |
Ratio between beta and its estimate. |
H_plus |
Initial upper limit of the CUSUM chart. |
a |
Tolerance level for the expected ARL (0 <= a < 1). |
b |
Tolerance level for the expected ARL (0 < b < 1). |
ARL_esp |
Desired expected ARL value. |
m |
Number of states in the Markov matrix. |
N_init |
Number of initial iterations. |
N_final |
Number of final iterations. |
known_alpha |
Indicates whether |
Value
A numeric value corresponding to the optimal H_delta
for the upward CUSUM control chart, ensuring the expected performance.
Examples
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)