Statistical inference and prediction for the Weibull process with incomplete observations

Authors:
Jun-Wu Yu;Guo-Liang Tian;Man-Lai Tang
Affiliations:
School of Mathematics and Computational Science, Hunan University of Science and Technology, Xiangtan, Hunan 411201, PR China;Division of Biostatistics, University of Maryland Greenebaum Cancer Center, 22 South Greene Street, Baltimore, MD 21201, USA;Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, PR China
Venue:
Computational Statistics & Data Analysis
Year:
2008

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Abstract

In this article, statistical inference and prediction analyses for the Weibull process with incomplete observations via classical approach are studied. Specifically, observations in the early developmental phase of a testing program cannot be observed. We derive the closed-form expressions for the maximum likelihood estimates of the parameters in both the failure- and time-truncated Weibull processes. Confidence interval and hypothesis testing for the parameters of interest are considered. In addition, predictive inferences on future failures and the goodness-of-fit test of the model are developed. Two real examples from an engine system development study and a Boeing air-conditioning system development study are presented to illustrate the proposed methodologies.