Repair alert model for one component systems with discrete lifetimes belonging to the power series family

Repair alert models are essential tools for optimizing preventive maintenance in engineering systems. However, the development of these models for systems with discrete lifetime measurements—such as operational cycles, weekly failure reports, or counts of pages printed—has not been systematically addressed under a general class of discrete lifetime distributions. This paper specifically addresses this research gap. We propose a comprehensive framework for repair alert modeling by assuming that the discrete lifetimes of devices belong to the “power series family” of distributions. This approach encompasses a wide class of practically relevant discrete distributions. As a key component of this framework, we address the parameter estimation challenges for three significant and well-known distributions within this family. The Akaike Information Criterion is employed for optimal model selection, and approximate confidence intervals for the parameters of the chosen distribution are derived. The validity and practical utility of the proposed model are demonstrated through an insightful analysis of a real dataset.