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Introduction: Accurately predicting the remaining mechanical equipment is of great significance for ensuring the safe operation of the equipment and improving economic efficiency. Methods: To accurately assess the mechanical equipment degradation, predict its remaining useful life, and ensure efficient, stable, and safe operation, a degradation and life prediction model for mechanical equipment based on multivariate stochastic processes is studied. The study innovatively predicts the remaining life of mechanical equipment using multivariate stochastic processes, and facilitates the correlation analysis between performance indicators based on the characteristics of Copula functions. Results and discussion: The results showed that the Root Mean Squared Error value of the prediction results based on the trivariate Wiener process was 2.58, which decreased by 46.91% and 35.82% compared with the univariate and bivariate Wiener processes, respectively. The prediction value based on the trivariate gamma process was 3.49, which decreased by 44.95% and 40.54% compared with the univariate and bivariate gamma processes, respectively. In conclusion, the degradation and life prediction model with multivariate stochastic processes can effectively assess the mechanical equipment degradation and predict its remaining useful life. This provides an important reference for the maintenance and management of mechanical equipment, improving equipment efficiency and extend its service life. [ABSTRACT FROM AUTHOR]

Background The application of foresight to the field of public health is limited. There is growing need to anticipate uncertain future trends and to plan for them. Foresight provides tools to experts and policymakers to discuss and plan for possible futures. Hence, the aim of this study is to illustrate how the foresight six-step approach can be applied in public health, and to provide recommendations on dealing with challenges, drawn from the Population Health Information Research Infrastructure (PHIRI) foresight exercise. Methods In this tutorial, we describe the six-step approach as part of foresight methodology and give examples of possible challenges. Step 1 comprises the formulation of study objectives. Step 2 focuses on developing a conceptual model and applying the Demographic Economic Sociocultural Technological Ecological and Political-Institutional (DESTEP) framework to identify and prioritize driving forces for the topic of interest. In Step 3, a time horizon and spatial level are defined. Step 4 discusses scenario logics. Steps 5 and 6 discuss different types of scenarios and associated tools for analyses. Possible challenges encountered whilst applying the foresight methodology at each of the steps, were drawn from experiences during PHIRI foresight exercise. Results Challenges associated with applying the foresight six-step approach included: formulating concise objectives, developing a conceptual model, understanding driving forces and uncertainty and difficulties in building scenarios. Conclusions Understanding concepts used in the six-step approach and how they relate to each other remained difficult. Support from foresight experts, conducting more foresight exercises, tutorials and guidelines can enhance understanding and support building capacity. [ABSTRACT FROM AUTHOR]