Due to the simplicity and flexibility of the power law process, it is widely used to model the failures of repairable systems. Although statistical inference on the parameters of the power law process has been well developed, numerous studies largely depend on complete failure data. A few methods on incomplete data are reported to process such data, but they are limited to their specific cases, especially to that where missing data occur at the early stage of the failures. No framework to handle generic scenarios is available. To overcome this problem, from the point of view of order statistics, the statistical inference of the power law process with incomplete data is established in this paper. The theoretical derivation is carried out and the case studies demonstrate and verify the proposed method. Order statistics offer an alternative to the statistical inference of the power law process with incomplete data as they can reformulate current studies on the left censored failure data and interval censored data in a unified framework. The results show that the proposed method has more flexibility and more applicability.

中文翻译：

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数据不完整的幂律过程的贝叶斯估计

由于幂律过程的简单性和灵活性，它被广泛用于对可修复系统的故障进行建模。尽管已经对幂律过程的参数进行了统计推断，但许多研究很大程度上依赖于完整的故障数据。据报告，有几种处理不完整数据的方法可以处理此类数据，但是它们仅限于特定情况，尤其是在故障早期出现丢失数据的情况下。没有可用于处理通用方案的框架。为了解决这个问题，从顺序统计的角度出发，建立了不完整数据的幂律过程的统计推断。进行了理论推导，并通过案例研究证明并验证了所提出的方法。订单统计可以用不完整的数据来替代幂律过程的统计推断，因为它们可以在统一的框架中重新整理对左删失数据和区间删失数据的当前研究。结果表明，该方法具有更大的灵活性和更大的适用性。