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Prediction in trend-renewal processes for repairable systems

机译：可修复系统的趋势更新过程预测

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摘要

Some problems of point and interval prediction in a trend-renewal process (TRP) are considered. TRP's, whose realizations depend on a renewal distribution as well as on a trend function, comprise the non-homogeneous Pois-son and renewal processes and serve as useful reliability models for repairable systems. For these processes, some possible ideas and methods for constructing the predicted next failure time and the prediction interval for the next failure time are presented. A method of constructing the predictors is also presented in the case when the renewal distribution of a TRP is unknown (and consequently, the likelihood function of this process is unknown). Using the prediction methods proposed, simulations are conducted to compare the predicted times and prediction intervals for a TRP with completely unknown renewal distribution with the corresponding results for the TRP with a Weibull renewal distribution and power law type trend function. The prediction methods are also applied to some real data.
机译：考虑了趋势更新过程（TRP）中的点和区间预测的一些问题。 TRP的实现取决于更新分布以及趋势函数，它包含非均匀的Poisson和更新过程，并作为可修复系统的有用可靠性模型。对于这些过程，提出了一些可能的构想和方法，用于构造预测的下一个故障时间和下一个故障时间的预测间隔。在未知的TRP更新分布（因此，此过程的似然函数未知）的情况下，还提供了一种构造预测变量的方法。使用提出的预测方法，进行仿真以将具有完全未知的更新分布的TRP的预测时间和预测间隔与具有Weibull更新分布和幂律类型趋势函数的TRP的相应结果进行比较。预测方法也适用于一些实际数据。

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