Preventive maintenance (PM) is a maintenance program with activities initiated at predetermined intervals, or according to prescribed criteria, and intended to reduce the probability of failure, or the degradation of the functioning of an item. In the literature, a number of PM models have been introduced to depict the effectiveness of PM. Based on these models, approaches to scheduling PM policies have been considerably studied. This paper attempts to review existing PM models, and investigate their inter-relationships. We then categorize these models into three classes: linear, nonlinear, and a hybrid of both. These three PM model classes depict the relationships of the hazard functions before, and after a PM. Possible extensions to these three PM models are discussed. The statistical properties for models are derived, and approaches to optimizing the PM policy are given.

The Paris agreement is a unified arrangement for the global response to climate change and entered into force on 4 November 2016. Its long-term goal is to hold the global average temperature rise well below 2 °C. China is committed to achieving carbon neutrality by 2060 through various measures, one of which is green technology innovation (GTI). This paper aims to analyze the levels of GTI in 30 provinces in mainland China between 2001 and 2019. It uses the spatial econometric models and panel threshold models along with the slack based measure (SBM) and Global Malmquist-Luenberger (GML) index to analyze the spatial spillover and nonlinear effects of GTI on regional carbon emissions. The results show that GTI achieves growth every year, but the innovation efficiency was low. China’s total carbon dioxide emissions were increasing at a marginal rate, but the carbon emission intensity was declining year by year. Carbon emissions were spatially correlated and show significant positive agglomeration characteristics. The spatial spillover of GTI plays an important role in reducing carbon dioxide emissions. In the underdeveloped regions in China, this emission reduction effect was even more significant.