Abstract
As a result of the two-parameter Birnbaum–Saunders (BS) distribution being successful in modelling fatigue failure times, several extensions of this model have been explored from different aspects. In this article, we consider a progressive stress accelerated life testing for the BS model to introduce a generalized Birnbaum–Saunders (we call it Type-II GBS) distribution on the lifetime of products in the test. We outline some interesting properties of this highly flexible distribution, present the Fisher’s information in the maximum likelihood estimation method, and propose a new Bayesian approach for inference. Simulation studies are carried out to assess the performance of the methods under various settings of parameter values and sample sizes. Real data are analyzed for illustrative purposes to demonstrate the efficiency and accuracy of the proposed Bayesian method over the likelihood-based procedure.
Highlights
The Birnbaum–Saunders (BS) model is based on a physical argument of cumulative damage that produces fatigue in materials, which is exerted by cyclical stress
We find that the rule of thumb cm = 15, c β = 2.4 as the tuning parameter values are adequate to ensure the acceptance rates to hover around 35–40%, and we run five Markov chain Monte Carlo (MCMC) chains with fairly different initial values and with a burn-in period of 2000 followed by 8000 iterations
We presented a Bayesian inference approach of parameter estimation in progressive stress accelerated life testing with the Birnbaum–Saunders (BS) model, which induced the Type-II
Summary
The Birnbaum–Saunders (BS) model is based on a physical argument of cumulative damage that produces fatigue in materials, which is exerted by cyclical stress. More research work has lied in the study of accelerated life testing (ALT) with the BS distribution In industrial experiments, it is often very costly and time consuming to obtain information about the lifetime of highly reliable products under normal experimental conditions. ALT where products or materials are subjected to elevated stress conditions compared to those normally applied in practice. An ALT on the BS distribution was considered in [14], who developed the model under the inverse power law accelerated form and explored the inference procedure based on the lifetime data collected under several elevated stress levels. To make a more efficient test plan for collecting the lifetime of highly reliable products, people usually resort to an ALT by a progressive stress, and we will consider such a model for the BS distribution
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