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Title: Parameter estimate with only one complete failure observation using Monte Carlo EM algorithm
Authors: Pang, WK
Leung, PK 
Xiao-Long, PU
Shi-Song, M
Keywords: EM algorithm
Failure data
Likelihood function
MCEM algorithm
Weibull distribution
Issue Date: 2001
Source: International journal of reliability, quality and safety engineering, 2001, v. 8, no. 2, p. 109-122 How to cite?
Journal: International Journal of Reliability, Quality and Safety Engineering 
Abstract: In reliability studies, often we only have one failure data recorded in a life testing experiment. If there are two parameters in the reliability model, such as the model using Weibull distribution, then maximum likelihood estimation of parameters becomes a difficult problem. Mao and Chen published a real data set of the lifetime of a certain type of bearings which only contains one failure data. They used a Bayesian method to analyze the data and obtained some results for model parameter estimation. However, in their method the choice of prior distribution will affect heavily the final results. In this paper, we propose a Monte Carlo EM (MCEM) algorithm to estimate reliability model parameters using the Weibull distribution. Based on the same data set of Mao and Chen, we obtain some results using the MCEM algorithm. Our results do not depend on the choice of arbitrary prior distributions.
ISSN: 0218-5393
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