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The purpose of this paper is to propose an uncertain regression model with an intrinsic error structure facilitated by an uncertain canonical process.
This model is suitable for dealing with expert's knowledge ranging from small to medium size data of impreciseness. In order to have a rigorous mathematical treatment on the new regression model, this paper establishes a series of new uncertainty concepts sequentially, such as uncertainty joint multivariate distribution, the uncertainty distribution of uncertainty product variables and uncertain covariance and correlation based on the axiomatic uncertainty theoretical foundation. Two examples are given for illustrating a small data regression analysis.
The uncertain regression model is formulated and the estimation of the model coefficients is developed.
The paper is devoted to a regression model to handle a small amount of data with mathematical rigor.
The theory and the methodology of the uncertain canonical process regression is proposed for the first time. It addresses the practical challenges of small data size modelling.
Intends to address a fundamental problem in maintenance engineering: how should the shutdown of a production system be scheduled? In this regard, intends to investigate a…
Intends to address a fundamental problem in maintenance engineering: how should the shutdown of a production system be scheduled? In this regard, intends to investigate a way to predict the next system failure time based on the system historical performances.
GM(1,1) model from the grey system theory and the fuzzy set statistics methodologies are used.
It was found out that the system next unexpected failure time can be predicted by grey system theory model as well as fuzzy set statistics methodology. Particularly, the grey modelling is more direct and less complicated in mathematical treatments.
Many maintenance models have developed but most of them are seeking optimality from the viewpoint of probabilistic theory. A new filtering theory based on grey system theory is introduced so that any actual system functioning (failure) time can be effectively partitioned into system characteristic functioning times and repair improvement (damage) times.
In today's highly competitive business world, the effectively address the production system's next failure time can guarantee the quality of the product and safely secure the delivery of product in schedule under contract. The grey filters have effectively addressed the next system failure time which is a function of chronological time of the production system, the system behaviour of near future is clearly shown so that management could utilize this state information for production and maintenance planning.
Provides a viewpoint on system failure‐repair predictions.