Quasi Renewal–Alpha Process Improves Failure Modeling for Systems Under Delayed Repair

A mathematical maintenance model based on a Quasi Renewal–Alpha Process provides a superior statistical fit over the classical Quasi Renewal Process for failure-time data from deteriorating systems subject to imperfect delayed repairs, according to an investigation published in Discover Applied Sciences. The framework addresses maintenance optimization in reliability engineering where repairs are imperfect and maintenance activities are subject to delays.

To evaluate equipment degradation under realistic maintenance constraints, the authors examined an N-failure replacement policy. Using renewal–reward theory, the researchers formulated explicit mathematical expressions to determine both the expected renewal cycle length and the long-run average cost rate associated with operating and repairing the deteriorating asset.

The study established formal analytical conditions that confirm the existence and uniqueness of an optimal replacement number under the proposed maintenance framework. Numerical examples are presented to illustrate the analytical results.

To assess the model against conventional maintenance frameworks, the team conducted an empirical comparison using a publicly available failure-time dataset. Comparative evaluation based on the Akaike Information Criterion demonstrated that the Quasi Renewal–Alpha Process provides a better fit than the classical Quasi Renewal Process for the analyzed dataset, confirming its effectiveness for modeling deteriorating systems experiencing imperfect repairs and maintenance delays.

Subject of Research: Maintenance optimization and replacement policies for deteriorating systems under imperfect delayed repair

Article Title: Optimal replacement policies for deteriorating systems under imperfect delayed repair via a quasi renewal–alpha process

Article References: Neelakandan, R., Iqbal, P., Babu, D., Sutha, M., & Mageswari, M. (2026). Optimal replacement policies for deteriorating systems under imperfect delayed repair via a quasi renewal–alpha process. Discover Applied Sciences. https://doi.org/10.1007/s42452-026-09506-z

Image Credits: AI Generated

DOI: 10.1007/s42452-026-09506-z

Keywords: reliability engineering, deteriorating systems, imperfect repair, delayed repair, maintenance optimization, replacement policies, Quasi Renewal-Alpha Process, Quasi Renewal Process, renewal-reward theory, N-failure replacement policy, expected renewal cycle length, long-run average cost rate, optimal replacement number, failure-time dataset, Akaike Information Criterion, repairable systems, statistical model fitting