Journal of Applied Mathematics and Decision Sciences
Volume 2007 (2007), Article ID 90842, 11 pages
Research Article

Weibull Model Allowing Nearly Instantaneous Failures

C. D. Lai,1 Michael B. C. Khoo,2 K. Muralidharan,3 and M. Xie4

1Institute of Information Sciences and Technology, Massey University, Palmerston North, New Zealand
2School of Mathematical Sciences, Universiti Sains Malaysia, Pulau Pinang 11800, Malaysia
3Department of Statistics, The Maharaja Sayajirao University of Baroda, Vadodara 390 002, India
4Department of Industrial and Systems Engineering, National University of Singapore, 119077, Singapore

Received 27 April 2007; Accepted 8 August 2007

Academic Editor: Paul Cowpertwait

Copyright © 2007 C. D. Lai 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.


A generalized Weibull model that allows instantaneous or early failures is modified so that the model can be expressed as a mixture of the uniform distribution and the Weibull distribution. Properties of the resulting distribution are derived; in particular, the probability density function, survival function, and the hazard rate function are obtained. Some selected plots of these functions are also presented. An R script was written to fit the model parameters. An application of the modified model is illustrated.