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A nonlinear Wiener process degradation model with autoregressive errors

机译：具有自回归误差的非线性Wiener过程退化模型

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摘要

Degradation information reflecting the product or system health state plays an important role in assessing reliability and making maintenance schedule. Since degradation inspections are usually compounded and contaminated by measurement errors in real applications, the conventional Wiener process with identically distributed independent Gaussian error is usually adopted. However, in many situations, autocorrelation may probably exist among the measurement errors at sequential test points because of cyclic changes or modeling errors, especially when the time intervals are relatively short. Motivated by this practical issue, a Wiener process degradation model with one-order autoregressive (AR(1)) measurement errors is proposed for degradation analysis. Explicit forms of the probability distribution function (PDF), the cumulative distribution function (CDF) and the corresponding mean time to failure (MTTF) are derived based on the concept of first hitting time (FHT). Furthermore, maximum likelihood estimations (MLE) of unknown parameters are derived. The effects of model mis-specification regarding the estimation of MTTF are also discussed. Finally, a comprehensive simulation study and two practical applications are given to demonstrate the necessity and efficiency of the proposed model. (C) 2017 Elsevier Ltd. All rights reserved.
机译：反映产品或系统健康状态的降级信息在评估可靠性和制定维护计划中起着重要作用。由于降级检查通常在实际应用中会因测量误差而加重和污染，因此通常采用具有均匀分布的独立高斯误差的常规维纳过程。但是，在许多情况下，由于循环变化或建模误差，尤其是在时间间隔较短时，在顺序测试点的测量误差之间可能存在自相关。受此实际问题的启发，提出了具有一阶自回归（AR（1））测量误差的Wiener过程退化模型，用于退化分析。基于首次击中时间（FHT）的概念，得出了概率分布函数（PDF），累积分布函数（CDF）和相应的平均失效时间（MTTF）的显式形式。此外，得出未知参数的最大似然估计（MLE）。还讨论了模型错误指定对估计MTTF的影响。最后，进行了全面的仿真研究和两个实际应用，以证明所提出模型的必要性和有效性。 （C）2017 Elsevier Ltd.保留所有权利。

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