GEOMETRIC - ALPHA PROCESS AND A MAINTENANCE MODEL FOR DETERIORATING SYSTEM

Abstract

The Geometric Process (GP) is a widely used stochastic model for analysing repairable systems with monotonic trends in successive inter-occurrence times. In this paper, we introduce the Geometric- Alpha Process (GAP), a new geometric-like process based on an alternative parametric formulation. Fundamental probabilistic properties of the GAP, including stochastic ordering and moment characteristics, are established, and a replacement model is formulated. The GAP is illustrated using the aircondit7 dataset, a benchmark reliability dataset containing operating times between failures of an aircraft air-conditioning system. For the analysed data, the GAP attains a higher maximized log-likelihood and a lower Akaike Information Criterion (AIC) than the classical GP, indicating a better fit.