Estimating Percentiles of Time-to-Failure Distribution Obtained from a Linear Degradation Model Using Kernel Density Method

Abstract

In this article, we propose a nonparametric estimator for percentiles of the time-to-failure distribution obtained from a linear degradation model using the kernel density method. The properties of the proposed kernel estimator are investigated and compared with well-known maximum likelihood and ordinary least squares estimators via a simulation technique. The mean squared error and the length of the bootstrap confidence interval are used as the basis criteria of the comparisons. The simulation study shows that the performance of the kernel estimator is acceptable as a general estimator. When the distribution of the data is assumed to be known, the maximum likelihood and ordinary least squares estimators perform better than the kernel estimator, while the kernel estimator is superior when the assumption of our knowledge of the data distribution is violated. A comparison among different estimators is achieved using a real data set.

Keywords:

• Bootstrap confidence interval
• Degradation
• Kernel density estimation
• Maximum likelihood estimator
• Ordinary least squares estimator
• Reliability

Mathematics Subject Classification:

• 62N02
• 62G07

Acknowledgments

The authors would like to thank the Editor in Chief, the referees, and Dr. Mohammed Al-Rawash for their valuable comments and suggestions that improved the content and the style of this article.