Help for package minimaxALT

Type:

Package

Title:

Generate Optimal Designs of Accelerated Life Test using PSO-Based Algorithm

Version:

1.0.0

Encoding:

UTF-8

License:

GPL (≥ 3)

Description:

A computationally efficient solution for generating optimal experimental designs in Accelerated Life Testing (ALT). Leveraging a Particle Swarm Optimization (PSO)-based hybrid algorithm, the package identifies optimal test plans that minimize estimation variance under specified failure models and stress profiles. For more detailed, see Lee et al. (2025), Optimal Robust Strategies for Accelerated Life Tests and Fatigue Testing of Polymer Composite Materials, submitted to Annals of Applied Statistics, https://imstat.org/journals-and-publications/annals-of-applied-statistics/annals-of-applied-statistics-next-issues/, and Hoang (2025), Model-Robust Minimax Design of Accelerated Life Tests via PSO-based Hybrid Algorithm, Master' Thesis, Unpublished.

SystemRequirements:

GNU Scientific Library (GSL), OpenMP

Imports:

Rcpp (≥ 1.0.11), RcppArmadillo (≥ 14.0.0.1), RcppGSL (≥ 0.3.13), ggplot2 (≥ 3.0.0), parallel (≥ 4.0.0), stats, graphics

Depends:

R (≥ 4.0.0)

LinkingTo:

Rcpp (≥ 1.0.11), RcppArmadillo (≥ 14.0.0.1), RcppGSL (≥ 0.3.13)

RoxygenNote:

7.3.2

URL:

https://github.com/hoanglinh171/minimaxALT

BugReports:

https://github.com/hoanglinh171/minimaxALT/issues

Suggests:

testthat (≥ 3.0.0)

Config/testthat/edition:

NeedsCompilation:

yes

Packaged:

2025-08-26 11:13:26 UTC; lu

Author:

Hoai-Linh Hoang [aut, cre], I-Chen Lee [aut], Ping-Yang Chen [aut], Ray-Bing Chen [aut], Weng Kee Wong [aut]

Maintainer:

Hoai-Linh Hoang <hoailinh.hoang17@gmail.com>

Repository:

CRAN

Date/Publication:

2025-09-01 09:30:02 UTC

minimaxALT: Generate Optimal Designs of Accelerated Life Test using PSO-Based Algorithm

Description

Author(s)

Maintainer: Hoai-Linh Hoang hoailinh.hoang17@gmail.com

Authors:

I-Chen Lee
Ping-Yang Chen
Ray-Bing Chen
Weng Kee Wong

Check Equivalence Theorem for Optimal Design

Description

Evaluates whether a design satisfies the equivalence theorem.

Usage

check_equivalence_theorem(best_particle, model_set, design_info, seed)

Arguments

best_particle

A vector containing the best particle's position (i.e., stress levels and transformed allocated proportion).

model_set

A matrix of models, including parameters and distribution, that maximize the optimality criteria with the given best particle's position.

design_info

A list containing design parameters such as factor levels, number of units, and other settings.

seed

Seed for reproducibility

Value

max_directional_derivative: Maximum directional derivative within design space.
model_set: The model set that is input.
model_weight: The weight assigned to each model in the model set.
equivalence_data: Generated designs and their corresponding directional derivative given the optimal design best_particle. Each design is a combination of factors with value in [0, 1]. These designs are data for plotting equivalence theorem plot.

References

Müller, C. H., & Pázman, A. (1998). Applications of necessary and sufficient conditions for maximin efficient designs. Metrika, 48, 1–19.
Huang, M.-N. L., & Lin, C.-S. (2006). Minimax and maximin efficient designs for estimating the location-shift parameter of parallel models with dual responses. Journal of Multivariate Analysis, 97(1), 198–210.

Examples

design_info <- set_design_info(k_levels=2, j_factor=1, n_unit=300, 
                               censor_time=183, p=0.1, use_cond=0, sigma=0.6)
                               
best_particle <- c(0.682, 1, 0.706)

model_set <- rbind(
  c(0.01, 0.9, 1),
  c(0.01, 0.99, 2))

equi <- check_equivalence_theorem (best_particle=best_particle, 
                                    model_set=model_set, 
                                    design_info=design_info,
                                    seed = 42)

equi$max_directional_derivative

Find Optimal ALT Design Using Hybrid Algorithm

Description

Runs hybrid algorithm combining PSO and Nelder-Mead to find the optimal design of accelerated life test (ALT).

Usage

find_optimal_alt(
  design_type,
  distribution,
  design_info,
  pso_info,
  coef = NULL,
  coef_lower = NULL,
  coef_upper = NULL,
  init_values = NULL,
  highest_level = TRUE,
  n_threads = 1,
  verbose = TRUE,
  seed
)

Arguments

design_type

Integer. 1: Locally optimal design, 2: Minimax design.

distribution

Integer. The assumed failure time distribution, 1: Weibull, 2: Log-normal, 3: Model robust (both distribution Weibull and Log-normal).

design_info

A list from 'set_design_info()' containing design specifications.

pso_info

A list from 'pso_setting()' defining PSO hyperparameters.

coef

Optional. Fixed model coefficients. Required if design_type = 1.

coef_lower

Optional. Lower bounds for model parameters. Required if design_type = 2.

coef_upper

Optional. Upper bounds for model parameters. Required if design_type = 2.

init_values

Optional. A list of initial values from 'initialize_values()'.

highest_level

Logical. Whether the highest stress level of the generated design is the upper bound of stress range x_h. Default value is TRUE.

n_threads

Integer. Number of threads for parallel processing.

verbose

Logical. If TRUE, print optimization progress.

seed

Integer. Seed for reproducibility

Value

g_best: The global best design found by the hybrid algorithm.
coef_best: The parameters corresponding to the global best design.
distribution_best: The distribution corresponding to the global best design.
max_directional_derivative: Maximum directional derivative within design space, evaluated using equivalence theorem.
fg_best: The objective function value corresponding to the global best design.
fg_best_hist: A vector tracking the best objective function value of each iteration.
p_best: A matrix containing each particle's personal best design found during the optimization.
fp_best: A vector containing the objective function values corresponding to each particle's personal best.
g_hist: All particle positions of each iteration.
coef_best_hist: The parameters corresponding to the global best designs of each iteration.
distribution_best_hist: The distribution corresponding to the global best designs of each iteration.
model_set: A matrix containing distribution and model parameters of global best particles of each iteration, duplicated models are removed.
model_weight: The weight assigned to each model in the model set.
equivalence_data: Generated designs and their corresponding directional derivative given the optimal design g_best. Each design is a combination of factors with value in [0, 1]. These designs are data for plotting equivalence theorem plot.

References

Chen P (2024). _globpso: Particle Swarm Optimization Algorithms and Differential Evolution for Minimization Problems_. R package version 1.2.1, <https://github.com/PingYangChen/globpso>.
Kennedy, J., & Eberhart, R. (1995). Particle swarm optimization. In Proceedings of the IEEE International Conference on Neural Networks (ICNN) (Vol. 4, pp. 1942–1948).
Lee, I. C., Chen, R. B., Wong, W. K., (in press). Optimal Robust Strategies for Accelerated Life Tests and Fatigue Testing of Polymer Composite Materials. Annals of Applied Statistics. <https://imstat.org/journals-and-publications/annals-of-applied-statistics/annals-of-applied-statistics-next-issues/>
Meeker, W. Q., & Escobar, L. A. (1998). Statistical methods for reliability data. New York: Wiley-Interscience.
Nelder, J. A. and Mead, R. (1965). A simplex algorithm for function minimization. Computer Journal, 7, 308–313. 10.1093/comjnl/7.4.308.

Examples

design_info <- set_design_info(k_levels=2, j_factor=1, n_unit=300, 
                               censor_time=183, p=0.1, use_cond=0, sigma=0.6)

pso_info <- pso_setting(n_swarm=32, max_iter=128, early_stopping=10, tol=0.01)

res <- find_optimal_alt(design_type=1, distribution=1, design_info=design_info, 
                        pso_info=pso_info, coef=c(0.001, 0.9), verbose = FALSE,
                        seed = 42)

summary(res)
plot(res, x_l=0, x_h=1)

Initialize Particle Swarm Optimization and Nelder-Mead Algorithm Values

Description

Sets initial particles for PSO, initial locally optimal design, and initial parameters for Nelder-Mead algorithm.

Usage

initialize_values(init_swarm = NULL, init_local = NULL, init_coef_mat = NULL)

Arguments

init_swarm

Optional matrix of initial particle positions. If not defined, particle positions are randomly generated using runif with pre-determined number of particles n_swarm and particle size.

init_local

Optional vector of initial locally optimal design. If not defined, the initial vector representing locally optimal design is c(1, 0.6, 0.3).

init_coef_mat

Optional matrix of initial parameters to implement multi-start Nelder-Mead algorithm. The number of rows is the number of starts, and each row is the corresponding initial parameters. If not defined, the initial matrix of parameters is generated by sigmoid transformation of 10 * as.matrix(expand.grid(rep(list(c(1, -1)), j_factor + 1))).

Value

A list of initialized values.

Examples

init_local <- c(1, 0.6, 0.3)

init_coef_mat <- rbind(
  c(1e-6, 0.99),
  c(1e-2, 1),
  c(1.01e-6, 0.9999))
  
j_factor <- 1
k_levels <- 3
n_swarm <- 32
d_swarm <- (j_factor + 1) * k_levels - 1
init_swarm <- matrix(runif(n_swarm*d_swarm), nrow=n_swarm, byrow=TRUE)

init_values <- initialize_values(init_swarm=init_swarm, 
                                  init_local=init_local, 
                                  init_coef_mat=init_coef_mat)

Set PSO Optimization Settings

Description

Define hyperparameters for particle swarm optimization (PSO).

Usage

pso_setting(
  n_swarm = 32,
  max_iter = 128,
  early_stopping = 10,
  tol = 0.01,
  c1 = 2.05,
  c2 = 2.05,
  w0 = 1.2,
  w1 = 0.2,
  w_var = 0.8,
  vk = 4
)

Arguments

n_swarm

Integer. Number of particles in the swarm.

max_iter

Integer. Maximum number of iterations.

early_stopping

Integer. The frequency, i.e. number of iterations, of validating the design optimality using equivalence theorem. The optimization process stops once maximum directional derivative is approximately 1.

tol

Numeric. Convergence tolerance. The algorithm stops if abs(max_directional_derivative - 1) < tol.

c1

Numeric. Cognitive acceleration coefficient. Default value is 2.05.

c2

Numeric. Social acceleration coefficient. Default value is 2.05.

w0

Numeric. Starting inertia weight. Default value is 1.2.

w1

Numeric. Ending inertia weight. Default value is 0.2.

w_var

Numeric. A number between [0, 1] that controls the percentage of iterations during which PSO linearly decrease inertia weight from w0 to w1. Default value is 0.8.

vk

Numeric. Velocity clamping factor. Default value is 4.

Value

A list of PSO hyperparameters.

Examples

pso_info <- pso_setting(n_swarm=32, max_iter=128, early_stopping=10, tol=0.01)

Set ALT Design Information

Description

Configures the settings for an accelerated life test.

Usage

set_design_info(
  k_levels,
  j_factor,
  n_unit,
  censor_time,
  p,
  use_cond,
  sigma,
  x_l = 0,
  x_h = 1,
  opt_type = "C",
  reparam = TRUE
)

Arguments

k_levels

Integer. Number of stress levels.

j_factor

Integer. Number of stress factors.

n_unit

Integer. Total number of test units.

censor_time

Numeric. Test duration or censoring time.

p

Numeric. 0 < p < 1. Lifetime percentile to be estimated at the use condition, i.e. stress levels are 0.

use_cond

Vector. Stress levels at the use condition.

sigma

Numeric. Scale parameter of the lifetime distribution.

x_l

Numeric. Lower bound of stress range. Default is 0.

x_h

Numeric. Upper bound of stress range. Default is 1.

opt_type

Character. Optimality criterion, currently only C-optimality is supported. Default is "C".

reparam

Logical. Whether reparameterization is applied to model parameters. Reparameterization is supported for all design types, while non-reparameterization is only available for locally optimal design design_type = 1. Default is TRUE.

Value

A list of design specifications

Examples

design_info <- set_design_info(k_levels=3, j_factor=1, n_unit=300, 
                           censor_time=183, p=0.1, use_cond=c(0), sigma=0.6)

minimaxALT: Generate Optimal Designs of Accelerated Life Test using PSO-Based Algorithm

Description

Author(s)

See Also

Check Equivalence Theorem for Optimal Design

Description

Usage

Arguments

Value

References

Examples

Find Optimal ALT Design Using Hybrid Algorithm

Description

Usage

Arguments

Value

References

Examples

Initialize Particle Swarm Optimization and Nelder-Mead Algorithm Values

Description

Usage

Arguments

Value

Examples

Set PSO Optimization Settings

Description

Usage

Arguments

Value

Examples

Set ALT Design Information

Description

Usage

Arguments

Value

Examples