Grey Duane model for reliability growth prediction under small sample uncertain failure data

Traditional reliability growth models require failure data to adhere to a specific distribution, which greatly limits the applicability in data-scarce scenarios. Drawing from the characteristic in modeling small sample and poor information of grey system theory, this study introduces a novel grey Duane reliability growth prediction model, tailored for analyzing uncertainty in limited failure data. The characteristics and adaptability of the proposed grey Duane model (GDM) are analyzed and compared with two traditional reliability growth prediction models. Utilizing a first-order accumulation generation operation, a differential function is established to estimate the unknown parameters in GDM. The proposed GDM enables synchronized predictions of failure time, failure number, and instantaneous mean time between failures. To validate the applicability of GDM in reliability growth management, an industrial case in particular electronic equipment during an aircraft's flight-testing process is applied, whose results demonstrate its superior predictive accuracy compared to alternative models.