Robust Estimation for Weibull Distribution in Partially Accelerated Life Tests with Early Failures |
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Authors: | Yung‐Fu Cheng Shey‐Huei Sheu |
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Affiliation: | 1. Graduate Institute of Science Education, National Taiwan Normal University, Taipei, Taiwan;2. Department of Statistics and Informatics Science, Providence University, Taichung, Taiwan;3. Department of Industrial Management, National Taiwan University of Science and Technology, Taipei, Taiwan |
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Abstract: | Maximum likelihood estimation (MLE) is a frequently used method for estimating distribution parameters in constant stress partially accelerated life tests (CS‐PALTs). However, using the MLE to estimate the parameters for a Weibull distribution may be problematic in CS‐PALTs. First, the equation for the shape parameter estimator derived from the log‐likelihood function is difficult to solve for the occurrence of nonlinear equations. Second, the sample size is typically not large in life tests. The MLE, a typical large‐sample inference method, may be unsuitable. Test items unsuitable for stress conditions may become early failures, which have extremely short lifetimes. The early failures may cause parameter estimate bias. For addressing early failures in the Weibull distribution in CS‐PALTs, we propose an M‐estimation method based on a Weibull Probability Plot (WPP) framework, which leads a closed‐form expression for the shape parameter estimator. We conducted a simulation study to compare the M‐estimation method with the MLE method. The results show that, with early‐failure samples, the M‐estimation method performs better than the MLE does. Copyright © 2015 John Wiley & Sons, Ltd. |
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Keywords: | constant stress partially accelerated life test WPP M‐estimation early failure |
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