Motivated by a real failure dataset in a two-dimensional context, this paper presents an extension of the Markov modulated Poisson process (MMPP) to two dimensions. The one-dimensional MMPP has been proposed for the modeling of dependent and non-exponential inter-failure times (in contexts as queuing, risk or reliability, among others). The novel two-dimensional MMPP allows for dependence between the two sequences of inter-failure times, while at the same time preserves the MMPP properties, marginally. The generalization is based on the Marshall-Olkin exponential distribution. Inference is undertaken for the new model through a method combining a matching moments approach with an Approximate Bayesian Computation (ABC) algorithm. The performance of the method is shown on simulated and real datasets representing times and distances covered between consecutive failures in a public transport company. For the real dataset, some quantities of importance associated with the reliability of the system are estimated as the probabilities and expected number of failures at different times and distances covered by trains until the occurrence of a failure.

翻译：基于实际二维失效数据集的动机，本文提出将马尔可夫调制泊松过程（MMPP）扩展至二维情形。一维MMPP已被用于建模相依且非指数失效间隔时间（应用于排队论、风险分析或可靠性等领域）。新型二维MMPP允许两个失效间隔时间序列之间存在相关性，同时边际上保持MMPP性质。该推广基于Marshall-Olkin指数分布。通过结合矩匹配方法与近似贝叶斯计算（ABC）算法对该新模型进行推断。基于仿真数据集及某公共交通公司连续故障间时间与距离的实际数据，验证了该方法的性能。针对实际数据集，估算了系统可靠性的若干重要指标，包括不同时间点及列车发生故障前行驶距离对应的故障概率与期望故障次数。