Abstract

Bathtub-shaped failure intensity is typical for large-scaled repairable systems with a number of different failure modes. Sometimes, repairable systems may exhibit a failure pattern different from the traditional bathtub shape, due to the existence of multiple failure modes. This study proposes two superposed Poisson process models with modified bathtub intensity functions to capture this kind of failure pattern. The new models are constructed by the superposition of the generalized Goel–Okumoto process and power law process (or log-linear process). The proposed models can be applied to masked failure-time data from repairable systems where the modes of collected failure-times are unobserved or unavailable. Bayesian posterior computation algorithms based on the data augmentation method are developed for the inference on the parameters or their functions of the superposed Poisson process models. This study also examines the best model selection among the candidate models in the Bayesian framework and modeling check using the residuals. A practical case study with a data set of unscheduled maintenance events for complex artillery systems illustrates potential applications of the proposed models for the purpose of reliability prediction for the repairable systems.

摘要

浴缸形状的故障强度对于具有许多不同故障模式的大型可修复系统来说是典型的。有时，由于存在多种故障模式，可修复系统可能会表现出与传统浴缸形状不同的故障模式。本研究提出了两个具有修正浴缸强度函数的叠加泊松过程模型来捕捉这种失效模式。新模型是通过广义 Goel-Okumoto 过程和幂律过程（或对数线性过程）的叠加构建的。所提出的模型可应用于来自可修复系统的掩蔽故障时间数据，其中收集的故障时间模式无法观察或不可用。开发了基于数据增强方法的贝叶斯后验计算算法，用于推断叠加泊松过程模型的参数或其函数。本研究还检查了贝叶斯框架中候选模型中的最佳模型选择，并使用残差进行建模检查。对复杂火炮系统的计划外维护事件数据集的实际案例研究说明了所提出的模型在可修复系统的可靠性预测方面的潜在应用。