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Reliability analysis using an exponential power model with bathtub-shaped failure rate function: a Bayes study.
Romana Shehla1, Athar Ali Khan1
1Department of Statistics and Operations Research, Aligarh Muslim University, 202002 Aligarh, India.
Springerplus
|July 28, 2016
Summary
This study explores the Bayesian analysis of the exponential power model, which can represent bathtub-shaped hazard functions. The research demonstrates straightforward Markov chain Monte Carlo simulations in R for reliability and medical applications.
Area of Science:
- Statistics
- Reliability Engineering
- Biostatistics
Background:
- Bathtub-shaped hazard functions are crucial in reliability and medicine for decision-making.
- The exponential power model offers flexibility in capturing various hazard shapes, including bathtub curves.
Purpose of the Study:
- To conduct a Bayesian analysis of the exponential power model.
- To demonstrate the application of Markov chain Monte Carlo (MCMC) methods in R for Bayesian inference.
- To extend the model with explanatory variables and provide practical R code examples.
Main Methods:
- Bayesian inference using weakly-informative priors.
- Posterior simulation via Markov chain Monte Carlo (MCMC) algorithms.
- Analysis of complete and censored data.
- Inclusion of continuous explanatory variables.
Main Results:
- The study successfully implements Bayesian analysis for the exponential power model.
- Posterior simulations using MCMC in R are shown to be efficient and routine.
- The model is extended to incorporate covariates, enhancing its applicability.
- Inference on non-linear functions of parameters is addressed.
Conclusions:
- The Bayesian approach with MCMC provides a robust framework for analyzing the exponential power model.
- The developed R tools facilitate practical application in reliability and medical studies.
- The extended model offers greater flexibility in analyzing complex data structures.
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