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Mathematical Problems in Engineering
Volume 2012, Article ID 953848, 11 pages
Research Article

Applying Hierarchical Bayesian Neural Network in Failure Time Prediction

1Department of Business Management, National Taipei University of Technology, 10608, Taiwan
2Graduate Institute of Industrial and Business Management, National Taipei University of Technology, 10608, Taiwan

Received 31 December 2011; Accepted 21 February 2012

Academic Editor: Jung-Fa Tsai

Copyright © 2012 Ling-Jing Kao and Hsin-Fen Chen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


With the rapid technology development and improvement, the product failure time prediction becomes an even harder task because only few failures in the product life tests are recorded. The classical statistical model relies on the asymptotic theory and cannot guarantee that the estimator has the finite sample property. To solve this problem, we apply the hierarchical Bayesian neural network (HBNN) approach to predict the failure time and utilize the Gibbs sampler of Markov chain Monte Carlo (MCMC) to estimate model parameters. In this proposed method, the hierarchical structure is specified to study the heterogeneity among products. Engineers can use the heterogeneity estimates to identify the causes of the quality differences and further enhance the product quality. In order to demonstrate the effectiveness of the proposed hierarchical Bayesian neural network model, the prediction performance of the proposed model is evaluated using multiple performance measurement criteria. Sensitivity analysis of the proposed model is also conducted using different number of hidden nodes and training sample sizes. The result shows that HBNN can provide not only the predictive distribution but also the heterogeneous parameter estimates for each path.