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Inference for accelerated test models based on failures or degradation data from cumulative damage processes.

机译：根据累积损坏过程中的故障或退化数据推断加速测试模型。

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摘要

This dissertation investigates some statistical problems in reliability theory. First, based on a discrete cumulative damage approach with a gamma process describing "initial damage" for a fibrous composite specimen, a new statistical model for the strength of such composites is developed. The model is an accelerated inverse Gaussian-type distribution and is shown to fit carbon composite strength data better than previous models. Asymptotic lower confidence bounds for percentiles of the strength distribution are obtained based on Bonferroni's inequality and the Fisher information. Simulation results indicate that the asymptotic Bonferroni lower bounds are quite conservative, and bootstrap methods for improving the bounds are considered. Then an example for observed tensile strengths of carbon micro-composites is presented.;Approximate lower confidence bounds on percentiles of the Weibull and the Birnbaum-Saunders distributions are investigated next. Asymptotic bounds based on Bonferroni's inequality and Fisher information are discussed, and parametric bootstrap methods are proposed to provide better bounds. Since the percentile bootstrap method typically does not perform well for confidence bounds on quantiles, other bootstrap procedures are studied via computer simulations. Results of the simulations indicate that the bootstrap methods generally give sharper lower bounds than the Bonferroni bounds but with coverages still near the nominal confidence level. Illustrative examples are given for carbon micro-composite specimen strength data and for cycles-to-failure data.;An important problem in reliability and survival analysis is that of modeling degradation together with any observed failures in a life test. Based on a continuous cumulative damage approach with a Gaussian process describing degradation, a general accelerated test model is presented in which failure times and degradation measures can be combined for inference about system lifetime. Some specific models when the drift of the Gaussian process depends on the acceleration variable are discussed in detail. Examples using simulated data as well as real data on degradation of carbon-film resistors are presented.;Finally, preliminary results on Bayesian estimation are given, and topics for future research are discussed.
机译：本文研究了可靠性理论中的一些统计问题。首先，基于离散累积损伤方法，用伽马方法描述了纤维复合材料试样的“初始损伤”，开发了这种复合材料强度的新统计模型。该模型是加速的逆高斯型分布，并且显示出比以前的模型更好地拟合碳复合强度数据。基于Bonferroni不等式和Fisher信息，获得强度分布百分数的渐近下置信界。仿真结果表明，渐近Bonferroni下界是相当保守的，并考虑了改进边界的自举方法。然后给出了一个观察到的碳微复合材料拉伸强度的例子。接下来研究了威布尔分布和百恩堡－桑德斯分布的百分位数的近似下置信界。讨论了基于Bonferroni不等式和Fisher信息的渐近边界，并提出了参数自举方法以提供更好的边界。由于百分位数自举方法对于分位数的置信范围通常表现不佳，因此通过计算机仿真研究了其他自举程序。仿真结果表明，自举方法通常比Bonferroni边界具有更窄的下界，但覆盖范围仍接近标称置信水平。给出了碳微复合材料样品强度数据和失效周期的说明性示例。可靠性和生存分析中的一个重要问题是建模退化以及在寿命测试中观察到的任何失败。基于具有描述退化的高斯过程的连续累积破坏方法，提出了一种通用的加速测试模型，其中可以组合故障时间和退化措施以推断系统寿命。详细讨论了当高斯过程的漂移取决于加速度变量时的一些特定模型。给出了使用模拟数据和真实数据进行碳膜电阻器退化的实例。最后，给出了贝叶斯估计的初步结果，并讨论了未来研究的主题。

著录项

  • 作者

    Tomlinson, Meredith Ann.;

  • 作者单位

    University of South Carolina.;

  • 授予单位 University of South Carolina.;
  • 学科 Statistics.
  • 学位 Ph.D.
  • 年度 2003
  • 页码 129 p.
  • 总页数 129
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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