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Mathematical Problems in Engineering
Volume 2015, Article ID 681232, 8 pages
Research Article

Weibull Failure Probability Estimation Based on Zero-Failure Data

1College of Information System and Management, National University of Defense Technology, Changsha 410073, China
2College of Continuing Education, National University of Defense Technology, Changsha 410073, China

Received 27 May 2014; Revised 4 September 2014; Accepted 15 October 2014

Academic Editor: Wenbin Wang

Copyright © 2015 Ping Jiang et al. 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.


Reliability testing is often carried out with small sample sizes and short duration because of increasing costs and the restriction of development time. Therefore, for highly reliable products, zero-failure data are often collected in such tests, which could not be used to evaluate reliability by traditional methods. To cope with this problem, the match distribution curve method was proposed by some researchers. The key step needed to exercise this method is to estimate the failure probability, which has yet to be solved in the case of the Weibull distribution. This paper presents a method to estimate the intervals of failure probability for the Weibull distribution by using the concavity or convexity and property of the distribution function. Furthermore, to use the method in practice, this paper proposes using the approximate value of the shape parameter determined by either engineering experience or by hypothesis testing through a p value. The estimation of the failure probability is thus calculated using a Bayesian approach. A numerical example is presented to validate the effectiveness and robustness of the method.