Change-point estimation for repairable systems combining bootstrap control charts and clustering analysis: Performance analysis and a case study

Abstract

Complex repairable systems with bathtub-shaped failure intensity will nor-mally go through three periods in the lifecycle, which requires maintenance policies and management decisions accordingly. Therefore, the accurate esti-mation of change points of different periods has great significance. This paper addresses the challenge of change-point estimation in failure processes for repairable systems, especially for sustained and gradual processes of change. The paper proposes a sectional model composed of two non-homogeneous Poisson processes (NHPPs) to describe the bathtub-shaped failure intensity. In order to obtain the accurate change-point estimator, a novel hybrid method is developed combining bootstrap control charts with the sequential cluster-ing approach. Through Monte Carlo simulations, the proposed change-point estimation method is compared with two powerful estimation procedures in various conditions. The results suggest that the proposed method performs effective and satisfactory for failure processes with no limits of distributions, changing ranges and sampling schemes. It especially provides higher preci-sion and lower uncertainty in detecting small shifts of change. Finally, a case study analysing real failure data from a heavy-duty CNC machine tool is pre-sented. The parameters of the proposed NHPP model are estimated. The change point of the early failure period and the random failure period is also calculated. These findings can contribute to determining the burn-in time in order to improve the reliability of the machine tool.