r2IGP

Overview

The r2IGP package is designed to provide engineers and researchers with a powerful tool for reliability analysis and degradation modeling, particularly using Two-Scale Reparameterized Inverse Gaussian Processes. This package offers a variety of features, including:

• Data Simulation: Generate simulated data that follows the Two-Scale Reparameterized Inverse Gaussian Process, ideal for reliability analysis and degradation modeling.

• Degradation Path Visualization: Allows users to visually display degradation paths, aiding in the analysis and understanding of the process.

• Statistical Inference: Provides methods for statistical inference across different models to estimate reliability and degradation characteristics from data.

• Reliability Analysis: Conduct in-depth reliability analysis of engineering systems or components, supporting a wide range of engineering applications.

Installation

You can install the development version of r2IGP from GitHub with:

# install.packages("devtools")
devtools::install_github("liangliangzhuang/r2IGP")

Get started

library(r2IGP)

It mainly includes the following functions:

• rIG Distribution: The random number generation, density function, and distribution generation for the rIG distribution are implemented in rrIG(), drIG(), and prIG(), respectively.

• Simulation: The function sim.dat.path() simulates a set of degradation models, with associated subfunctions including Lambda_cum(), Lambda_fun(), and Lambda_fun_der().

• Statistical Inference for Models: Statistical inference for the five models using the EM algorithm or MLE is implemented in EM(). Relevant subfunctions include:

  • E-step Integration: The E_z() function performs E-step integration, using three approximation methods due to the lack of a closed-form solution:

    • Trapezoidal Approximation: trapezoidal_integral().

    • Monte Carlo Integration: mc_integral().

    • Gauss-Legendre Quadrature: gaussian_legendre_integral().

Other functions for likelihood evaluation include f_uz_given_D_gaussian(), Log.likelihood(), M4.loglik(), Integrand_fun(), and init.log.likelihood().

• Interval estimation: Interval estimates for the models are computed using bootstrap methods in CI_Bootstrap(), with support for parallel computing to accelerate execution.

• Plotting: Contains various visualization functions, primarily for displaying degradation paths and EM iteration progress. Notable functions include path.3D.plot(), fit.path.plot(), degradation.path.plot.summary(), and EM_iter_plot().

• Reliability: Contains functions for reliability analysis, focusing on the computation of reliability over time based on different models. The two key functions are: uncon_lifetime_CDF(), Reliability().

• Miscellaneous: Others functions contain such as selected_fun() and save.result().