Bayesian Estimation of the Mean Time Between Failures of Subsystems with Different Causes Using Interval-Censored System Maintenance Data
Abstract
Ensuring an acceptable level of reliability stands as a primary imperative for any mission-focused operation since it serves as a critical determinant of success. Inadequate reliability can lead to severe repercussions, including substantial expenses for repairs and replacements, missed opportunities, service disruptions, and, in the worst cases, safety violations and human casualties. Within national defense organizations such as the USAF, the precise assessment and maintenance of system reliability play a pivotal role in ensuring the success of mission-critical operations. In this research, our primary objective is to model the reliability of repairable subsystems within the framework of competing and complementary risks. Subsequently, we construct the overall reliability of the entire repairable system, utilizing day-to-day group-censored maintenance data from two identical aircraft systems. Assuming that the lifetimes of subsystems follow non-identical exponential distributions, it is theoretically justified that the system reliability can be modeled by homogeneous Poisson processes even though the number of subsystems of any particular type is unknown and the temporal order of multiple subsystem failures within a given time interval is uncertain due to interval censoring. Using the proposed model, we formulate the likelihood function for the mean time between failures of subsystems with different causes, and subsequently establish an inferential procedure for the model parameters. Given a considerable number of parameters to estimate, we explore the efficacy of a Bayesian approach, treating the contractor-supplied estimates as the hyperparameters of prior distributions. This approach mitigates potential model uncertainty as well as the practical limitation of a frequentist-based approach. It also facilitates continuous updates of the estimates as new maintenance data become available.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 15, 2024
- Accession Number
- AD1230178
Entities
People
- David K. Han
- James D. Brownlow
- Jesse E. Thompson
- Ralph G. Brooks
Organizations
- United States Air Force